An additional or fourth name given by the Romans, on account of some remarkable exploit or event; as, Publius Caius Scipio Africanus.

An additional name, or an epithet appended to a name; as, Aristides the Just.

An Agnomen is a nickname. It is not a pseudonym as it is a real name, but an agnomen is usually a name in addition and not a substitution for the real name. For example, Aristides "the Just" or "Iron" Mike Tyson.