last name vs surname

last name and surname both are nouns.

Word	Noun	Adjective	Verb	Adverb
last name	Yes	No	No	No
surname	Yes	No	No	No

As nouns, last name and surname are synonyms defined as:

last name and surname: the name used to identify the members of a family (as distinguished from each member's given name)

Other synonyms of last name include cognomen, family name.

last name (noun)	surname (noun)
the name used to identify the members of a family (as distinguished from each member's given name)	the name used to identify the members of a family (as distinguished from each member's given name)