If you've studied advanced mathematics, you've certainly read or at least heard about the books and papers of the great French mathematician Nicolas Bourbaki, whose works in the 1930's set out a rigorous formulation of modern mathematics. Except he never actually existed. The name was created as a front for a group of renegade French mathematicians who were reacting to Poincaré's intuitive approach.
In modern graph theory, I'm told that it is fashionable to publish one's results under false names. For example, the graph theorist G. W. Peck was actually a collaboration of the mathematicians Ronald Graham, Douglas West, George Purdy, the legendary Paul Erdős, Fan Chung, and Daniel Kleitman. (Take the initials of the members' last names.) I learned from Dr. West that the group did not include him originally, and they were prepared to publish under the name "G. Peck", listing the author's address as Hollywood, California. With the addition of a new member, the name changed to "G. W. Peck", which to the group's pleasant surprise happened to be the name of a United States Congressman from the 19th century, which gave them the opportunity to include a photograph and a short biography that ended with something like "After retiring from Congress, Peck returned to his first love: graph theory."