Idk anyone who complains about that, I know a few Americans who are born to German and Italian immigrant parents and even in our friends circle we only jokingly say “Oh the Americans came”, otherwise we refer to them and they to themselves as German and Italian.

Europeans tend to keep to their “origins” even if they move abroad or are born in a different country than their parents were from.

So if I end up moving to Germany, but both my wife and I are Italian, the children will consider themselves Italians, not German. Sure, some might take it and call themselves German but not all.