I have Northern Italian friends who consider themselves very separate to the Southern Italians. The Lega Nord party was originally about Padania (Northern Italy) separatism.
Northern or Southern? What about your ancestry prior to the existence of Italy?
And what does that mean, anyway? That some people in your family were born inside some arbitrary lines drawn on the ground? Who cares?
This sort of classification is meaningless.
(I, too, have Italian ancestry, but that's a small part of the overall picture, and has little to do with anything "real" about me, like my health or looks.)
And that's the intersection between race, genetic background, ethnicity, heritage, and culture.
You joke, but "assigned at birth" is probably apt. You may have discomfort or comfort in identifying with it. It may subtly change your perceptions and perceptions of you.