What is a name used by an author instead of his real name?

That is usually called a "pen name." Sometimes people will refer to it as "nom de plume" which essentially means the same thing, only in French. Generally, another good term to know is "pseudonym" which is what a person would call any fake name someone uses. So one could say "He published the book under a pen name" or could also say "He published the book under a pseudonym/."