I've always been in favor of the Washington Tribe. It's not specifically Native American, but definitely pays tribute to the history of the team. And it also alludes to community, both on the team and with the fans. Plus if you want to get way into feel-good gobbledygook, it would be the only team in the league with a singular name; not "Tribes" but "Tribe" suggesting that we are all one people. Seems like a good PR move.
That would be the infamous Dupont Circle. Insider tip; 20th to Q to 19th, or take Connecticut Ave right under it.