Washington Rhiggers.
Or, Washington Sunburns.
I submit that you stumbled upon the correct answer with this!
The Washington Whatevers would appeal to apathetic folks everywhere. It would also be kind of a tounge-in-cheek protest to the PC crowd. It’s bland, unoffensive, uncreative, and a stupid compromise that symbolizes so much of what happens in DC.
The “logo” wouldn’t even be a logo. Random symbols, images, words, whatevers, would be printed on each shirt, each jersey, each helmet, and so on.
If someone wants to start bashing the team from Washington, fans can just reply with “Whatever!” 
It has so many advantages.
Maybe their mascots could be General Apathy and Major Boredom.
Washington Bureaucrats.
Okay, it’s boring, but let’s face it: 50% of the folks in the DC metro area are exactly that one way or another.
And they would be hated by the rest of the country. That’s a rivalry every team owner dreams of!
It’s nice to see Congress addressing vital issues like this since all other problems facing the nation have been neatly disposed of by our hard-working legislators.
May Congress indulge in airborne coitus with a mobile toroid pastry.
The Washington Crackers? The Washington Honkeys? The Washington Imperial Wizards?
No, wait… The Washington Whiteys!
Since they no longer play in DC proper, how about the PG Gangstas or the PG Thugz?
My dad always called them the Washington Foreskins.
Yes, he was a Cowboys fan, why do you ask?
The Washington Leeches. Their mascot can be a congressman.
Moved Cafe Society --> the Game Room.
The Washington Bullets.
It’s available.
mmm
We just call them the Landover Racial Epithets.
The Washington Gay Scouts.
The Washington Sprawl
Actually, it’s not.
The baseball team is the Washington Nationals
The hockey team is the Washington Capitals (do they still exist? ETA: they do!)
The basketball team is the Washington Wizards
Washington Irvings
“The District Of Columbia Redskins”
OH I love that!
The Washington Irvings
Made my morning RobDog
As someone from Potomac, I have trouble reconciling the idea of big, professional athletes with the upper class snobs and spoiled little princessess they’ve spawned that are native to Potomac, MD.
Gregg Easterbrook insists on “Potomac Drainage Basin Indigenous Persons”.
I’d go with Skins, with a new logo not containing Indian symbols.
Or Lobbyists - “Didja see the way the Lobs took out the Iggles yesterday?”