I imagine the Right-wing would be something like True Patriots, or even just Patriots, they got a lot of rings.
What would the left call themselves? It wouldn't be anything Patriotic, because Americas history is... problematic. It'd have to be something sorta jingoistic though to get people to join and be interested, as there aren't enough radicals on either side to really make up any kind of force. Something like the New Dawn Coalition, or maybe The Real Revolutionaries. I dunno, hard to think like them.