License the right to use the Shawnee name from the Tribe. Thinking of Tecumseh, here. Their historic territory was in and around Maryland and Northern Virginia.
Or another historically fierce Tribe. Pay for the privilege, like the Florida State Seminoles do.
Or go with Arrows, as another poster suggested.
Probably not “Arrows” - since they already got rid of one name reflecting deadly weapons - “Bullets” for their basketball team.
I thought it was because they weren’t making their shots. 
The Washington Lobbyists?
“Tonight, see the Bears go at the Lobbyists!”
“Oh, hell, yeah!”
“He was a Lobbyist; now he’s a Buccaneer.”
“So, sort of a lateral move, there.”
“Today, it’s the Lobbyists versus the Patriots!”
“What else is new?”
As a Chiefs fan, I don’t think the Braves are likely the last refuge of the politically incorrect. I’d be sad to see the name changed, but it wouldn’t kill me. I would be happy to see the Tomahawk Chop be punishable by exile to Broncos-fandom, though.
Washington Wankers?
Or how about Spartans? Just sayin’ as an MSU alum.
The Washington Monuments. They’re big, they cost a lot, there’s nothing besides gravity holding them together, and they’re never going anywhere.
Definitely. Who has the REAL power in DC?
I think the Foggy Bottoms has a nice ring to it.
The Diplomats name has been the name of two different Washington-based soccer teams: one in the NASL in the 1970s/80s, the other in a couple of pro leagues from '88-'90. So, the name has some familiarity in the Washington area, plus it’s probably available. And, even better, it lends itself to the nickname “the Dips.” 
Washington Warmongers
The Washington Swamps. You can’t drain the Swamps!
There are no “Seahawks” either but that didn’t prevent the NFL’s franchise in Seattle from using that name.
I was just discussing renaming with Mrs. J. (a consultant of great perspicacity) and we settled on the Washington Reparations* and Cleveland Rocks.**
*since Washington is a divisive figure, better go with D.C. Reparations.
**or a return to the historic Cleveland Spiders.
**Having a tough time with a name to replace the Braves. The Atlanta Aarons?
I shared this and the peanut gallery lolled.
They then contributed “The Deep State”.
Which initial got typed as The Derp State.
Go back a ways before Atlanta, before Milwaukee, before they were the Boston Braves, they were the Boston Beaneaters.
They’re ornithologists?
Brainstorming here:
The Washington Sunburns… okay, maybe not. Still, there’s another line of thought here…
The Washington Carcinomas… or heck, just The Washington Cancers
Are you expecting them to get two more draft picks?
:flees: