nickname vs cognomen

nickname and cognomen both are nouns.

Word	Noun	Adjective	Verb	Adverb
nickname	Yes	No	Yes	No
cognomen	Yes	No	No	No

As nouns, nickname and cognomen are synonyms defined as:

nickname and cognomen: a familiar name for a person (often a shortened version of a person's given name)

Other synonyms of nickname include byname, moniker, sobriquet, soubriquet.

nickname (noun)	cognomen (noun)
a familiar name for a person (often a shortened version of a person's given name)	the name used to identify the members of a family (as distinguished from each member's given name)
a descriptive name for a place or thing	a familiar name for a person (often a shortened version of a person's given name)

nickname (verb)	cognomen (verb)
give a nickname to