Maiden Names vs. Married Names Is there a set convention for which name (maiden name or married name) a female married mathematician should use? 
While this question addresses women's maiden name it applies equally to men's maiden name when it differs from their married name. The question seeks for an advice for the dilemma: whether to use the maiden name or the new married name. 
For example, Fan Chung is married to Ron Graham, but she publishes under "Fan Chung."  Vera T. Sós is another married woman who continued to use her maiden name, but the T. stands for Turán.  Yet, I'm pretty sure that Emma Lehmer (née Trotskaia) published under her married name.  
Does it have something to do with the name under which the woman first publishes or the name under which name she receives her Ph.D.?
 A: As with other questions of this type, it is best to ask your community.  While the MathOverflow community is still deciding on whether to serve mathematicians by taking on such questions, originally it was (and many think still) intended exclusively for research level questions about mathematics.  This question is not of that kind.
The reason to ask your community (advisors, fellow students, mentors) is that the results  (which name will you choose for publishing) will most likely apply to it, and you will be judged by the community based on your choices and actions.  (This is assuming you have no firm position on the issue, otherwise why ask?)  The MathOverflow community is not that community, and will judge you differently if it judges you at all.  (Please note that the current debate is about the question, not about the asker.)
I suggest asking a different community.  There is an Association for Women in Mathematics, many of whose members (if not all) have maiden names.  I bet their collective experience is more valuable than many of the responses you will get here.  They may also be part of a community you will join (presuming you were a maiden and are intending to keep your gender).  Hopefully others will provide other communities for which your question will be appropriate.
Good Luck, and congratulations.
Gerhard "My Maiden Name Is Paseman" Paseman, 2011.08.31
A: Like all questions involving names and marriage, there is no set convention (at least in the US).  I know a male mathematician who publishes under his wife's last name which he took at marriage and I know people who have started publishing under a new name before they took it legally.  As Ben says, there's also no rules for names that don't involve marriage: not only do people pick whether they use their full first name or a nickname, some people use initials, and some people use nicknames which are not related to their legal first name.
Although there are no set rules or conventions, most people seem to agree that early on in your career it's unwise to change the name that you are publishing under.  Your name is your brand and diluting it is likely to hurt you professionally.  Thus there's a strong tendency for people to publish under a fixed name.  Nonetheless this is not a fixed rule, a particularly striking example is a theorem that's changed names: Nichols-Richmond nee Nichols-Zoeller.
A: There are numerous different circumstances when people marry and/or change their names.  There is clearly no general rule on this, as the question hints already.  Let me describe the ways.  
First, conventions.   There are not two but really four types of surnames we are talking about:
a) full legal name (usually found in passports)
b) professional name (university websites, wikipedia)
c) pen name (used to author papers, see arXiv, mathscinet)
d) maiden names and other former names
I believe neither two have to be the same, some people have more than one version of at least one of these items (say, have two passports from different countries, or publish under two different names, whatever), and occasionally people have different all four. 
EXAMPLES


*

*a) Julia Hall Bowman Robinson,  b),c) Julia Robinson, d) Julia Bowman

*b) Sofia Kovalevskaya, c) Sophie Kowalevski, d) Sofia Vasilyevna Korvin-Krukovsky  
as for a), I am not sure if there was a passport back then; if issued today she would have a passport in the name Sofia Vasilyevna Kovalevskaya (modern transliteration, changed several times)

*a),b)  Mary Ellen Rudin,  d) Mary Ellen Estill, c) published first as Estill, then as Rudin

*a),b),c) Cathleen Synge Morawetz, d) Cathleen Synge  (published also with S. as an initial) 

*a) Ruth Elke Lawrence-Naimark, b),d) Ruth Elke Lawrence, c) Ruth Lawrence

*a),b) Dmitry Feichtner-Kozlov, c),d) Dmitry N. Kozlov (although Russian passport is notoriously difficult to change, and usually continues to have maiden name).  

*a),b),c) Lane A. Hemaspaandra, d) Lane A. Hemachandra (this is an example of this trend sometimes considered bogus)
Browsing here will give you many more different examples.  For legal background in the US, see here.  
P.S.  To further appreciate complexity arising sometimes, consider e.g. this explanation by Paco Santos (ht Gil Kalai).  
A: No matter how futile this discussion is, I would still like to emphasize its insufferable sexism. It's a real shame it addresses female mathematicians only. Igor's answer provides an example (number 6) of real universality of this problem (those who are not in command of Russian may have not realized that the person in question is actually male). Another example is Dave Morris. To quote his home page, My older publications list "Dave Witte" as the author, but I changed my name when I married Joy Morris in December 2002". 
