pen name vs anonym

pen name and anonym both are nouns.

Word	Noun	Adjective	Verb	Adverb
pen name	Yes	No	No	No
anonym	Yes	No	No	No

As nouns, anonym is a hypernym of pen name; that is, anonym is a word with a broader meaning than pen name:

pen name: an author's pseudonym
anonym: a fictitious name used when the person performs a particular social role

Other hypernyms of pen name include nom de guerre, pseudonym.

pen name (noun)	anonym (noun)
an author's pseudonym	a fictitious name used when the person performs a particular social role