I s'pose somebody could come up with the American (the continent) equivalent of 'Azania', a word that related more to the peoples that inhabited it before the Europeans went in. But it would never catch on and... it wouldn't apply to most of us in any event. Most of us down there are mongrels, the product of the atrocities that the Spanish, in particularly, committed, which resulted in a mix of 'races' (there's another slippery concept) European, indigenous and black. That I think is actually a good thing.
Maybe I should stop replying with things like 'You're American? ah, I'm American too. My part of the continent was America before yours was'. There's no point. It's a long lost battle. It would only antagonise people who often are warm, lovely peeps (at least the ones I know here; we'll leave Trump supporters for another discussion).