false name vs assumed name

false name and assumed name both are nouns.

Word	Noun	Adjective	Verb	Adverb
false name	Yes	No	No	No
assumed name	Yes	No	No	No

As nouns, false name and assumed name are synonyms defined as:

Other synonyms of false name include alias.

false name (noun)	assumed name (noun)
a name that has been assumed	a name that has been assumed
	(law) a name under which a corporation conducts business that is not the legal name of the corporation as shown in its articles of incorporation