I understand it is, but like... I live in an area that has a lot of people with Scottish and Irish last names, and while it's obvious that at some point our ancestors came from Ireland or Scotland, only about 10% of the population would self-identify as such. (Co-incidentally, most of us are Roman Catholic too, go figure.)

Also, there's a whole different type of history for the last names of African Americans, y'know? Couple generations back somebody on his father's side of the family was probably owned by someone with the last name Mahoney.

tl;dr Just because someone's surname denotes a certain culture/nationality does not automatically mean said person identifies with that culture/nationality, etc etc etc. :-)