This is all impossible to say and really up to the individual.
If I take one of those Ancestry DNA things, I'm gonna come back French on my dad's side. We're not French. The town we're from used to be Germany. We came over when it was Germany. Then it became France - it was a war thing. I consider myself German. If you insisted I'm French, I guess you're not technically incorrect and I wouldn't be mad about it.
On my mom's side we're from Liverpool in the UK by way of Ireland. I consider myself Irish-Scouse. I will get mad if you call me English.
Some members of my own family might disagree with the identity I have described because it's how I choose to identify.
I'm also American but ethnically and culturally, that means nothing to me. The US is a big country. I have nothing in common with people from the South, Midwest, Pacific Coast, etc. I consider myself a New Yorker more than an American. Again, members of my own family will tell you different and being American is their entire personality.