Definition: An agnomen (pl. agnomina) could be part of Roman names as an added on cognomen. The Roman name is taken to be typically a tria nomina or 3-name, consisting of a praenomen or given name, a nomen gentile or gentilicium (the clan name), and a cognomen specifying the family within the clan. After these might come an added cognomen or agnomen -- or more than one.
Examples:
In the name Publius Cornelius Scipio Aemilianus Africanus, "Africanus" is an agnomen won for his conquests in Africa.