Agnomen

n. 4th name given to a citizen of ancient Rome (as an honor); additional cognomen given to a Roman citizen; nickname

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.Agnomina like "Britannicus" or "Nero" were used in ancient Rome to distinguish between similarly-named members of a family, or to honour of impressive accomplishments. For example, Coriolanus earned his from the capture of Corioli. See Roman naming convention.
See more at Wikipedia.org...

n. agnomen

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

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

N
nickname| an additional name denoting an achievement/characteristic