cognomen vs nickname

cognomen and nickname both are nouns.

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

As nouns, cognomen and nickname are synonyms defined as:

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

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

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

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