The history of John Rainwater can be read at the following link: http://at.yorku.ca/t/o/p/d/47.htm He has 10 published articles and several unpublished ones, by varying authors from the University of Washington.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."