cognomen vs moniker

cognomen and moniker both are nouns.

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

As nouns, cognomen and moniker are synonyms defined as:

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

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

cognomen (noun)	moniker (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)