At times. It was more of a regional phenomenon. Once[some still do] it was I'm a Virginian, a Tennessean. Texas perhaps carries that tradition today.
yes, but that moniker was not used to glean welfare status or a financial advantage, it was merely a cultural sense of pride and friendly competition.
Within the country, maybe. For the rest of the world, you’re an American.
I’m a New Yorker, but I certainly don’t introduce myself to foreigners that way, even though they obviously know where New York is - and they have their own regional divisions, in fact.