Pseudonyms of famous mathematicians Many mathematicians know that Lewis Carroll was quite a good mathematician, who wrote about logic (paradoxes) and determinants. He found an expansion formula, which bears his real name (Charles Lutwidge) Dodgson. Needless to say, L. Carroll was his pseudonym, used in literature.
Another (alive) mathematician writes under his real name and under a pseudonym (John B. Goode). (That person, by the way, is Bruno Poizat: it's no secret, even MathSciNet knows it.)

What other mathematicians (say dead ones) had a pseudonym, either within their mathematical activity, or in a parallel career ?

Of course, don't count people who changed name at some moment of their life because of marriage, persecution, conversion, and so on.

Edit.
The answers and comments suggest that there are at least four categories of pseudonyms, which don't exhaust all situations.


*

*Professional mathematicians, who did something outside of mathematics under a pseudonym (F. Hausdorff - Paul Mongré, E. Temple Bell - John Taine),

*People doing mathematics under a pseudonym, and something else under their real name (Sophie Germain - M. Le Blanc, W. S. Gosset - Student)),

*Professional mathematicians writing mathematics under both their real name and a pseudonym (B. Poizat - John B. Goode),

*Collaborative pseudonyms (Bourbaki, Blanche Descartes)

 A: From Zinbiel, G.W., Encyclopedia of types of algebras 2010, Bai, Chengming (ed.) et al., Operads and universal algebra. Proceedings of the summer school and international conference, Tianjin, China, July 5--9, 2010. Hackensack, NJ: World Scientific (ISBN 978-981-4365-11-6/hbk; 978-981-4458-33-7/ebook). Nankai Series in Pure, Applied Mathematics and Theoretical Physics 9, 217-297 (2012). ZBL1351.17001.:
"Note that J.-L. Loday published this article under the pseudonym Guillaume William Zinbiel (Zinbiel is Leibniz written backwards)."
A: William Sealy Gosset published a result under the pseudonym 
Student.
(Because his employer, the Guinness brewing company, did not allow their employees to publish for fear of divulging trade secrets.)
A: D. P. Parent is the author of a book of Exercises in Number Theory. 
Its authors are D. Barsky, F. Bertrandias, G. Christol, A. Decomps, H. Delange, J.-M. Deshouillers, K. Gérardin, J. Lagrange, J.-L. Nicolas, M. Pathiaux, G. Rauzy and M. Waldschmidt.
The initials of the pseudonym recall the names of Delange, Pisot and Poitou,
the three organizers of a Number Theory Seminar in Paris, which runs since 1959. 
A: Hugo Steinhaus was also an author of aphorisms, which he published in the daily "Slowo Polskie" under a pseudonym Sestertius.  Most were just goofy definitions of everyday terms. The following example seems to do OK in translation from Polish: "An opinion that all high-rank officers are stupid: a generalization".  The book edition ("Slownik Racjonalny") appeared in 1980 (after his death) under his real name.  
A: Elena Ventzel is not a very famous mathematician, although her textbook on Probability for engineers was (still is?) by far the most famous and widely used one in Russia.
She had a successful separate career as a fiction writer under a pen-name I. Grekova (derived from "igrek").
A: It might be a stretch but Ben Franklin spent time on recreational mathematics https://en.wikipedia.org/wiki/Magic_square, https://www.amazon.com/Benjamin-Franklins-Numbers-Mathematical-Odyssey/dp/0691129568/, and called himself a number of pseudonyms (Richard Saunders, Mrs. Silence Dogood) in his other writings.
A: In addition to being the "G" of G. W. Peck (as pointed out by Richard Stanley earlier), Ron Graham also published "On properties of a well-known graph or What is your Ramsey number?" as Tom Odda, a member of the Department of Mathematics from Xanadu University.
Apparently the name was chosen because if said quickly it sounded like the Chinese expression 他妈的 pronounced "ta ma de", a not so polite phrase in Chinese!
A: D'Alembert's name was in a sense a "pseudonym." D'Alembert was abandoned as an infant. However, d'Alembert was neither the name of his birth parents nor his adoptive parents. He made it up when he was a student.
A: Boto von Querenburg wrote a book on general topology, which is one of the standard source in German. According to Wikipedia the name actually stands for the authors Gunter Bengel, Hans-Dieter Coldewey, Klaus Funcke, Edelgard Gramberg, Norbert Peczynski, Andreas Stieglitz, Elmar Vogt and Heiner Zieschang. The name Boto was chosen as an abbreviation of "Bochum topologists" and the University of Bochum is in a part of the town called Querenburg. 
A: Felix Hausdorff published philosophical and literary books as Paul Mongré.
Let me mention that Hausdorff committed suicide (along with his wife) in 1942, to prevent his being sent to a concentration camp. He had tried to escape to the US, but unfortunately no one would sponsor him. So he joined the ranks of mathematicians who were victims of World War II (including some Germans who died at Soviet hands, for example Gentzen). 
A: O. P. Lossers has published since 1965, mostly problem solutions in various journals.  He has Erdös number 2.  
A: T. G. L. Zetters, has proven in 1979 that either player can draw in the 8-in-a-row game.  This is a variant of the well known 5-in-a-row where players take turn placing their mark to a square on an infinite square grid, and a player wins if they have a consecutive sequence of 8 or more of his own marks in a row, column, or diagonal.  According to the book Csákány Béla, Diszkrét Matematikai Játékok (Polygon, Szeged, 1998), this is a pseudonim of a group of Dutch mathematicians.  According to the manuscript András Csernenszky, The Chooser-Picker 7-in-a-row-game (submitted in 2010, arXiv:1004.2460v1), it is a pseudonym for A. Brouwer.  
A: One may type "pseudonym" into an "Anywhere" box at MathSciNet and find 44 hits. Many of these are not relevant to the question at hand, but I'll post any that I find that haven't been posted here already. Here's one: Christian Tapp, Kardinalitat und Kardinale, MR 2006h:01012, the review by Volker Peckhaus says that in Chapter 5, "We learn about [Georg] Cantor's pseudonyms such as Vincent Regnas, Jorge Vincente Monteador de Montemor, and others...." 
A: The mathematician Dan Barbilian was also a poet, having the pen name Ion Barbu. Some of his works are described here (Wayback Machine) and here (Wayback Machine).
A: Albert Gifi is a  group pseudonym for a groupf of authors writing "Nonlinear Multivariate Analysis" From this Wikipedia page:
https://en.wikipedia.org/wiki/Jan_de_Leeuw
"De Leeuw is the originator[4] of the Albert Gifi team that wrote Nonlinear Multivariate Analysis.[5] In Multidimensional Scaling, Volume 1,[6] Cox and Cox write that "Albert Gifi is the nom de plume of members, past and present, of the Department of Data Theory at the University of Leiden who devised a system of nonlinear multivariate analysis that extends various techniques, such as principal components analysis and canonical correlation analysis."   "
A: I guess, though I am not sure, the case of Albert Wormstein falls in your third category: 
Professional mathematicians writing mathematics under both their real name and a pseudonym.  
This paper: "Polyominoes of order 3 do not exist" (Journal of Combinatorial Theory, Series A, Volume 61, Issue 1, September 1992, Pages 130–136) has been written by I. N. Stewart and A. Wormstein. 
Here is the story behind the paper as told by Ian Stewart himself. 

The link has the correct story. Albert Wormstein first appeared in one of my articles for Pour La Science /
  Scientific American, which was used as a chapter in the cited book. 
  While I was writing that article it suddenly seemed clear that there
  ought to be a way to prove the conjecture about order 3 polyominoes.
  It felt as though Albert was tapping me on the shoulder and saying
  'come on, we can do this.' It quickly turned out he was right. So I
  decided to give him credit as a co-author. The journal either spotted
  the joke and went along with it, or they assumed Albert was a PhD
  student. At any rate, they published it with him as co-author.

A: P. A. Batnik was a pseudonym used by Paul T. Bateman and Bruce Reznick for contributions to the American Math Monthly's problems column. See, e.g., http://celebratio.org/Bateman_PT/article/332/
A: According to the review of  Reinhard Siegmund-Schultze, Sørensen, Henrik Kragh, Louis Olivier: a mathematician only known through his publications in Crelle’s journal during the 1820s, Centaurus 48, No. 3, 201-231 (2006). ZBL1115.01012., "ventures several hypotheses, including that ‘Olivier’ was a pseudonym. From the information revealed in this article the reviewer is inclined not even to rule out that Olivier and Crelle were the same person." 
A: Gergonne has published 43 additional papers anonymously or under a pseudonym in his Annales des Mathématiques pure et appliquée (1810–1831). In his copy of the journal given to the Sorbonne library, he had added his name manually to these contributions (see Henry, C., Supplément à la bibliographie de Gergonne., Bonc. Bull. 14, 211-218 (1881). JFM 13.0019.01.).
A: For reasons that it amuses him not to explain, Harold Simmons published the book First Steps in Modal Logic under the pseudonym Sally Popkorn.
A: Rainich=Rabinowitsch (of  trick fame :  cf. Nullstellensatz). 
Here is an anecdote related by Bruce P. Palka, Editor of American Mathematical Monthly
in Vol.111 (2004) of that journal (page460).
Rainich was giving a lecture in which he made use of a clever trick which he had discovered. Someone in the audience indignantly interrupted him pointing out that this was the famous Rabinowitsch trick and berating Rainich for claiming to have discovered it. Without a word Rainich turned to the blackboard, picked up the chalk, and wrote
                    RABINOWITSCH

He then put down the chalk, picked up an eraser and began erasing letters. When he was done what remained was
                   RA IN  I CH

He then went on with his lecture.
EDIT: There is some additional information (located by  Sándor Kovács) to be found at jstor.org/pss/4145123. We reproduce the relevant section below:

"Lance also contributes some new information to the saga of the elusive Mr. Rabinowitsch (see the Editor's Endnotes in the May 2004 issue): Poor Rabinowitsch, whoever he may be. The correct reference is: J. L. Rabinowitsch, "Zum Hilbertschen Nullstellensatz", Math. Ann. 102 (1930), p.520. In various places his first initial is either "A" or "S." On my trip to the library, I saw that Rainich had published in the Annalen under his own name and from Ann Arbor the previous year. Why a pseudonym?" The mystery deepens a bit in a biography of Rainich, where it's mentioned that he was born Rabinowitsch. On the same theme, Herman Roelants of Leuven, Belgium, points out that a Rabinowitsch anecdote similar to the one in the May 2004 MONTHLY is found on page 959 of the MONTHLY paper "Reminiscences of an Octagenarian Mathematican" by L. J. Mordell (November, 1971). Herman goes on to say that details concerning this source, together with references to important number-theoretic work of Rabinowitsch, can be found in the text and in a footnote on page 108 of Richard A. Mollin's book Quadratics (CRC Press, 1996).”

A: G. W. Peck originally was the pseudonym of Ronald Graham, Douglas West, George B. Purdy, Paul Erdős, Fan Chung, and Daniel Kleitman. Since then G. W. Peck was the author of sixteen publications, most by Kleitman alone. See https://en.wikipedia.org/wiki/G._W._Peck.
A: Continuing to troll through MathSciNet, I find Yu I Krivonosov, Higher mathematics and higher authority, MR 2002k:01034, reviewed by R L Cooke (and I highly recommend the review). It seems that A I Lapin, a convicted anti-Soviet agitator, confined to an asylum in Leningrad, was allowed to publish under a pseudonym in 1952. 
A: Yet another find on MathSciNet. Anita Feferman, Politics, Logic, and Love, MR 93j:01010, reviewed by D J Struik. This is a biography of Jean van Heijenoort. "In 1948 he broke openly with his past in a paper of [sic] the Partisan Review, where he denied the scientific nature of Marxism. He wrote it under a pseudonym (Jean Vannier) - after all he was an alien and it was the McCarthy period." 
A: Here's one more from MathSciNet. N Ya Vilenkin, Formulas on cardboard, MR 93a:01039, reviewed by B Rosenfeld. Nikolay S Koshlyakov was arrested in 1942, was denounced as an "enemy of the nation," and was condemned to ten years in the camps. The book written by him in the camp, Investigations of a class of transcendental functions determined by the generalized equation of Riemann, was published ... in 1949 ... under the pseudonym N S Sergeev (Koshlyakov's patronymic name was Sergeevich). 
A: Heinrich Seidel's review of M Lothaire, Combinatorics on Words, MR 84g:05002, says "The name of the author is a pseudonym chosen by the mathematicians who together with D Perrin serve as coauthors." There are about a dozen coauthors. 
A: The review by E Reich of I J Good and K Caj Doog, A paradox concerning rate of information, MR 19, 1245h, informs us that "The name of the second author is understood to be a pseudonym." 
A: As far as I know, Horst Herrlich has some publications as Y.T. Rhineghost.
http://www.informatik.uni-bremen.de/~herrlich/public/index.html (Wayback Machine)
http://www.csupomona.edu/~hlord/geist/ (Wayback Machine)
I do not know the story behind this pseudonym.
A: Although some think of Pythagoras as one person, it is now thought that his name is used for geometric and number theoretical discoveries made by anonymous members of his sect.
Thus, we can think of "Pythagoras" as the pseudonym of a collective of Greek intellectuals from about 500 BCE.
A: Jacob Goodman published the as-yet-unsolved Pancake Problem under the pseudonym, Harry Dweighter ("harried waiter"). See, e.g., https://faculty.math.illinois.edu/~west/openp/pancake.html
A: I realize now that Oscar Zariski was only a variation of his original name Ascher Zaritsky. He changed his name when publishing his dissertation, perhaps to hide his Jewish origin in the fascist Italy.
A: A very common type of pseudonym, especially in the Renaissance, was a Latinisation. Examples include:


*

*René Descartes becomes Renatus Cartesius;

*Mikołaj Kopernik becomes Nicolaus Copernicus;

*Geert de Kremer becomes Gerardus Mercator;

*Willebrord Snel van Royen ('Snell') becomes Willebrord Snellius.


(Mathematics was not as well-established as a single profession at the time, and most of the people listed were active in many fields of science. A true Renaissance scientist is a polymath.)
Remark. For some reason, this practice seems to have been especially popular in the Low Countries. This is somewhat remarkable, given that (following Simon Stevin, another Renaissance scientist) the Dutch language dropped Latin and Greek loanwords like subtract, multiply, and even mathematics itself, in favour of the Dutch words aftrekken, vermenigvuldigen, and wiskunde. There are very few European languages that have their own word for mathematics.
Remark. One may argue that a Latinisation does not constitute a pseudonym, but if we translate pseudonym literally as false name, then any name deviating from a person's actual [legal] name can be considered a pseudonym.
A: Pytheas N. Fogg is a collective of several authors including Valérie Berthé, Sébastien Ferenczi, Christian Mauduit, Anne Siegel and others - Review of J. P. Allouche of 
Pytheas Fogg, N. (ed.); Berthé, Valérie (ed.); Ferenczi, Sébastien (ed.); Mauduit, Christian (ed.); Siegel, A. (ed.), Substitutions in dynamics, arithmetics and combinatorics, Lecture Notes in Mathematics. 1794. Berlin: Springer. xv, 402 p. EUR 57.95/net; sFr. 96.50; £ 40.50; $ 76.80 (2002). ZBL1014.11015.: "This collective book, published under the pseudonym N. Pytheas Fogg, based on courses given by the authors in several universities and during several summer schools".
A: "Madame Veuve Prime/Madame F. Prime" was most likely a pseudonym (see Eneström, G., Questions 41 48. Remark on the question 43, Bibl. Math. (2) VII. 31-32, 64, 96, 120 (1893); (2) VIII. 32, 63-64, 96, 120 (1894) (1893,1894). ZBL25.0011.05.), but so far no one seems to have identified the author. 
A: Peter Cameron tells the story of the collaborative pseudonym WE Opencomb in his (Peter’s) blog 
https://cameroncounts.wordpress.com/2009/10/28/collaboration-in-mathematics/
A: Isaac Newton, in his dabblings in alchemy, called himself Jehovah Sanctus Unus.  http://science.howstuffworks.com/dictionary/famous-scientists/physicists/isaac-newton3.htm
A: Siegel published The integer solutions of the equation $y^2=ax^n+bx^{n-1}+\cdots+k$, J London Math Soc 1 (1926) 66-68, under the pseudonym, X. 
Anecdotal evidence of a non-pseudonym: Once when Littlewood attended an international conference in France, a French mathematician greeted him: “So there really is a Littlewood, and it is not just a pseudonym which G.H. Hardy uses to publish his poorer papers!”
A: Shalosh B. Ekhad, hmm, not sure if that's exactly a pseudonym but it sort of fits this discussion.
A: Another find on MathSciNet. Dominique Descotes, Genese des corollaires 1 et 2 de la lettre à Carcavy de Blaise Pascal, MR 99g:01016, review by Craig Fraser: In December of 1658 Blaise Pascal began to publish under the pseudonym A Dettonville the mathematical work Lettres de A Dettonville.... According to C B Boyer, "the name Amos Dettonville was an anagram of Louis de Montalte, the pseudonym used [by Pascal] in the Lettres provinciales." 
A: In addition to K.M.S. Humak mentioned earlier (which encodes "Kollektiv Mathematische Statistik: Humboldt-Universität zu Berlin und Akademie der Wissenschaften der DDR"), Helga Bunke had a long-term career in literature under her maiden name Helga Königsdorf.
A: Andersen, Kirsti; Meyer, Henrik, Georg Mohr’s three books and the Gegenübung auf Compendium Euclidis Curiosi, Centaurus 28, 139-144 (1985). ZBL0571.01014. discusses the identity of J.D.S., author of "Gegenübung auf Compendium Euclidis Curiosi (1673)", and are convinced that it is not (as assumed by Bierens de Haan) a pseudonym of Georg Mohr (hence, the real identity seems still open). 
A: Gohierre de Longchamps used the pseudonym Elgé for publications in Journal de mathématiques élémentaires and Journal de mathématiques spéciales of which he was editor, see
Lazzeri, G., Gastone Gohierre de Longchamps, Periodico di Mat. (3) 4, 53-59 (1906). ZBL37.0031.04.
A: Since some of those mentioned in other answers are among the living, let me also mention Victor Kac and his teacher Ernest Vinberg.   They published a joint paper Spinors of 13-dimensional space in Advances in Mathematics 30 (1978) under the rather transparent pseudonyms V. Gatti and E. Viniberghi.   As I recall, Victor said that this came about because he had applied for an exit visa from the USSR and was therefore not allowed to publish anything in the interim.   
A: Maurizio Boyarski = Bernard Dwork. Even mathscinet knows about that. Does anyone know why Dwork published under a pseudonym?
Dwork, Bernard: On the Boyarsky principle. Amer. J. Math. 105 (1983)
Boyarsky, Maurizio: p-adic gamma functions and Dwork cohomology. Trans. Amer. Math. Soc. 257 (1980)
A: Noga Alon published half a dozen papers under the name "A. Nilli".  Mathscinet links directly from this pseudonym to Noga's publications.
A: D. H. J. Polymath is a pseudonym for a collective of mathematicians (some of them may be not professional mathematicians).
A: A. Weil published two short papers/letters signed as X.X.X (Amer. J. Math. 79, 1957, 951-952) and R. Lipschitz (Ann. of Math. 69, 1959, 247-251) where he posed as an anonymous correspondent and the XIX century German mathematician residing in Hades respectively. Both letters are reprinted at the very end of the second volume of Weil's Collected papers.
A: Niccolò Fontana best known as Tartaglia.
A: According to Daniel Lazard, in his review of Berenstein and Struppa, Recent improvements in the complexity of the effective nullstellensatz, MR 92m:13024, N Fitchas was a pseudonym for a working group led by J Heintz that got results on the membership problem and the representation problem. 
A: Volume 1 of Statistical Methods of Model Building, edited by Helga Bunke and Olaf Bunke, was first published under the pseudonym of K M S Humak. See the review by J Kleffe, MR 88d:62121. See also MR 86b:62002. 
A: Noaï Fitchas was a pseudonym for the group of Joos Heintz and his students Leandro Caniglia, Guillermo Cortiñas, Silvia Danón, Teresa Krick, and Pablo Solernó.
A: Endre Weiszfeld, a childhood friend of Erdős, changed his name to Andrew Vázsonyi to escape persecution as a Jew. But much later, he also used the alias Zepartzatt Gozinto, at least for this book review. The story goes that the name arose when he made a joke in a talk and George Dantzig misheard it.
A: "Mathematician" might be a slight stretch, but math-related and of real-world significance: no one has yet figured out who Satoshi Nakamoto is.
A: The history of John Rainwater can be read at the following link: http://at.yorku.ca/t/o/p/d/47.htm (Wayback Machine) He has 10 published articles and several unpublished ones, by varying authors from the University of Washington. The same page also mentions in passing three other mathematical pseudonyms: P. Orno, M. G. Stanley, and H. C. Enoses.
John Rainwater came into existence at the University of Washington in 1952 when Nick Massey, a mathematics graduate student in Prof. Maynard Arsove's beginning real variables class, erroneously received a blank registration card. (In those years, each student filled out a card for every class, which first circulated among various tabulating clerks in the registrar's office before being sent to the professor.) He and a fellow graduate student, Sam Saunders, decided to use the card to enroll a fictional student, and since it was raining at the time, decided to call him "John Rainwater". They handed in John Rainwater's homework regularly, so it wasn't until after the first midterm exam that Prof. Arsove became aware of the deception. He took it well, even when he later opened an "exploding" fountain pen with John Rainwater's name engraved on it which had been left on the classroom table.
[...]
The first of John Rainwater's ten published research papers were written in 1958 and 1959 by John Isbell, a young Assistant Professor. Isbell's response to queries concerning his motivation for using J.R. as a pseudonym has been simply to quote Friedrich Schiller "Der Mensch ist nur da ganz Mensch, wo er spielt."
A: At the height of fascist persecution of Jews, Federigo Enriques penned some of his articles as Adriano Giovannini (reputedly coined from the names of his daughter Adriana and of his son Giovanni), as a device to circulate them. I was able to trace back to that pseudonym at least two papers: "Il pensiero di Galileo Galilei" and "L'errore nelle matematiche". 
As I understand it, that is to be considered a pseudonym used just in publications rather than a fully new name for real life, so I deemed the answer qualifying with regard to the question requirements.
Also, not being able to comment others' answers, I can add von Neumann as good example of the category depicted in Andreas' answer.
A: Heisuke Hironaka published a result on complex analysis in one variable (see Remmert's "Classical topics in complex function theory", chapter 5) in 1965 under the name Iss'sa. Apparently the name is a reference to a Japanese poet.
A: The paper "Why You Cannot Even Hope to Use Gröbner Bases in Public-Key Cryptography? An Open Letter to a Scientist Who Failed and a Challenge to Those Who Have Not Yet Failed" by Boo Barkee ,  Julia Ecks ,  Theo Moriarty ,  R. F. Ree: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.7134
The lead author is Moss Sweedler.  Boo Barkee was the name of his dog (so does this count as a pseudonym :-)?).
A: Arthur L. Besse - after the round tables held at Besse in France. (The "L." is for Lancelot.)
Edit
From Wikipedia, Arthur Besse is a pseudonym chosen by a group of French differential geometers, led by Marcel Berger, following the model of Nicolas Bourbaki. A number of monographs have appeared under the name.
A: Does Plato count?  (No pun entirely intended.)
A: Křesomysl Blizzard https://zbmath.org/authors/blizzard.kresomysl was a pseudonym of the collective of Walter Schachermayer, Erik G. F. Thomas and Heinrich von Weizsäcker for the publication
Blizzard, Křesomysl, A Krein-Milman set without the integral representation property., Frolík, Zdeněk (ed.), Abstracta. 8th winter school on abstract analysis. Abstracts of papers presented at the winter school, WSAA 8, Moravská Bouda, Czech Republic, 1980. Prague: Czechoslovak Academy of Sciences. 39-42 (1980). ZBL1437.46007.
Note that the DML CZ https://dml.cz/handle/10338.dmlcz/701173 did only partially resolve the identity as E.G.F. Thomas with the remark "Author corrected, K. Blizzard did not participated at the school"; the full identity is given in [20] of Schachermeyer's homepage https://www.mat.univie.ac.at/~schachermayer/pubs/index.php.
A: E. S. Pondiczery was a pseudonym used by R. P. Boas, Jr. in the paper Power problems in abstract spaces. The name became part of the well-known Hewitt-Marczewski-Pondiczery theorem (Wayback Machine).
Another pseudonym used by Boas (and F. Smithies) was H. Pétard. I highly recommend that you take a look at the hilarious Lion hunting and other mathematical pursuits (A collection of mathematics, verse, and stories by the late Ralph P. Boas, Jr.) for more information in this regard.
Added (Nov 7/2010). In that book you can also learn about other pseudonyms (for instance, Ian Stewart's one) and the memorable feud 'twixt Bourbaki and Boas.
Added (Nov 8/2010). According to page 10 of the aforementioned book, H. Pétard was in fact a pseudonym that Boas and Smithies made up for the use of E. S. Pondiczery. 
A: I'm surprised that no one named Leonardo of Pisa, known as Fibonacci to us (though he didn't use this nickname, and its origin is not completely clear).
Al-Khoresmi is apparently a nickname as well (though this time used by the author), meaning his origin.
(Maybe not exactly an answer to the original question, because these are rather nicknames, not pseudonyms.)
A: When it became dangerous for Jacques Feldbau to publish under this own (Jewish) name, he briefly wrote under the name Jacques Laboureur before being captured by the Nazis.  See Weil's Souvenir d'apprentissage or the commetaries in his Collected papers.  See also Une histoire de Jacques Feldbau by Michèle Audin, her article in the Images des Mathématiques and Jean Cerf's article (Wayback Machine) in the Gazette.
A: Eric Temple Bell (known for Bell numbers, series, polynomials, as well as his book Men of mathematics) wrote sci-fi novels using pseudonym John Taine.
A: Henri-Paul de Saint Gervais is a collective pseudonym of fifteen mathematicians
who recently published a book, Uniformisation des surfaces de Riemann, retour sur un
théorème centenaire, about the uniformization of Riemann surfaces.
(presentation of the book, in French).
They met in Saint-Gervais to work on the book, hence the lastname.
The firstname, Henri-Paul, reminds of Henri Poincaré and Paul Koebe, of course!
By the way, this book is highly recommended !
A: I'm not sure whether to count as pseudonyms the altered names that people took (often to avoid antisemitic prejudice) as replacements for their real names.  For example, Alfred Tarski's last name was originally Tajtelbaum, and Edward Marczewski's last name was originally Szpilrajn.  There must be lots of other examples of this sort.
A: MR 23 #A2744 reads, 
Schark, I. J. 
Maximal ideals in an algebra of bounded analytic functions. 
“I. J. Schark” is a pseudonym for the group: Irving Kaplansky, John Wermer, Shizuo Kakutani, R. Creighton Buck, Halsey Royden, Andrew Gleason, Richard Arens and Kenneth Hoffman. J. Math. Mech. 10 1961
A: "Smooth Manifolds and Observables" by
Jet Nestruev. 
The actual team of
Authors: A. M. Astashev, A. V. Bocharov, S. V. Duzhin, A. B. Sossinsky, A. M. Vinogradov, M. M. Vinogradov 
Springer-Verlag, Graduate Texts in Mathematics, vol. 220, 2002
A Russian answer to Bourbaki (see the preface to the book). 
A: Monsieur Antoine Auguste Le Blanc. (Sophie Germain, 1776–1831)
Sophie Germain hid behind the male pseudonym "M. Le Blanc" to study at the École Polytechnique and to be taken seriously in mail correspondence with other mathematicians, including Lagrange and Gauss.
A: In the 1980's there were a few papers by Bill Moran, William G. Hoover and Stronzo Bestiale; the most famous is http://williamhoover.info/Scans1980s/1987-3.pdf
If you read italian, it will be obvious for you that there is something wrong with the last name. There is a legend that the first two authors were so upset about the third co-author, that they replaced his true name with this one: see http://web.archive.org/web/20091026050929/http://individual.utoronto.ca/scharf/bizarre.htm.
The paper went through the whole refereeing and publishing process!
A: *

*Thomas Young (of diffraction, elasticity, and Rosetta Stone fame) published mathematics as


*

*Emeritus

*Hydrophilus

*Apsophus

*Dytiscus

*Hemerobius

*A. B. C. D.

*E. F. G. H.

*S. B. L.


*Norbert Wiener published The Miracle of the Broom Closet and The Brain as W. Norbert.

*James Joseph Sylvester (itself an adopted surname) published papers as Lanavicensis.

*Michel Rolle (d’Ambert) was Remi Lochell (de Bertam) in polemics against the calculus.

*William Roberts published several papers as M. Strebor.

*Joseph Liouville was his own alleged correspondent M. Besge (Neuenschwander, p. 60).

*Pascual Jordan (of quantum mechanics, Jordan algebras fame) expressed “extreme far-right political views” under the pseudonym Ernst Domeier.
A: André Bloch was an active mathematician during his stay (1918-1948) in a psychiatric asylum. During WWII, he wrote under the pseudos René Binaud and Marcel Segond, to hide his Jewish name.
A: Joseph Bernstein published a paper under the pseudonym "Yantarov" (which is derived from the Russian
translation of the German word "Bernstein" which means "amber").
At the time of writing he was an "otkaznik", a person waiting for permission to emigrate from the USSR,
and a paper under his own name would not be accepted. 
A: Levi Ben Gershon (1288-1344) (see also here) is commonly known to us as the RaLBa"G. Again, this is a nickname rather than a pseudonym- RLBG = "Rabbi Levi Ben Gershon", much in the same way as Shah Rikh Khan is known as SRK.
He wrote three mathematics books including Maaseh Hoshev, which "... is notable for its early use of proof by mathematical induction, and pioneering work in combinatorics. " 
