cognomen
1. [ noun ] a familiar name for a person (often a shortened version of a person's given name)
Synonyms: nickname soubriquet sobriquet moniker
Examples:

"Joe's mother would not use his nickname and always called him Joseph" "Henry's nickname was Slim"

Related terms: appellation dub
2. [ noun ] the name used to identify the members of a family (as distinguished from each member's given name)
Synonyms: family_name last_name surname
Related terms: name maiden_name