Synonyms for Cognomen (same or very similar meaning)
WordNet sense 1 (a familiar name for a person (often a shortened version of a person's given name)):
moniker, nickname, sobriquet, soubriquet, byname
WordNet sense 2 (the name used to identify the members of a family (as distinguished from each member's given name)):
surname, family name, last name
From the ODE community, based on WordNet
add/edit