A pseudonym is a name that someone, often a writer, uses instead of their real name. The real name of Dr. Seuss was Theodore Seuss Geisel. Mark Twain was a pseudonym for the writer Samuel Clemens.
A near synonym of pseudonym is pen name. Similarly, an allonym is the name of an important person in history that is taken by a writer as a pseudonym. Some of Shakespeare's plays might have been written by other writers using an allonym. If an actor uses a fake name, it is usually called a stage name. And there's no fancy work for nickname — it's just what your family and friends call you.