I don't think that "The Washington Expos" will work. Too much like "unnamed sources." No, wait, that's a great name!

If not the Senators, my personal choice is either the "Nationals", which also has a venerable DC history, or the name of a bird.

The Washington Titwillows.
The Washington Bluebirds.
The Washington Sparrows.
The Washington Vultures.
The Washington Dodoes.
The Washington Archiopteryxes.
The Washington Nightengales.
The Washington Magpies.
The Washington Oriol...no, no. Not that.

Anyway, the list of possibilities is extensive and just consider the possible nicknames!!!!