Other than the name, the rest of the logo is pretty great. A few too many stripes here and there and the type clashes a little bit with the rest of the aesthetic but that's nothing compared to how much the name clashes with everything. At this point it seems like they're just ignoring the name altogether; might as well change it up!
You could make arguments for a ton of names that would fit here: Senators, Diplomats (the Dips!), Generals, etc. The Washington Generals are already that-team-that-plays-against-the-Globetrotters, so that's out. We like the Monuments as the most direct tie to the logo, but really anything would be an improvement. We kept the foundational elements, streamlined the outer circle, skinny-d up the stars to get closer to the original Washington family crest, and drew some new letters inspired by some of the plaques on the Washington Monument.
We downgraded the silver in the color palette, extended the stone cut lettering to the numbers, and added a secondary logo that combines a basketball with the Washington family crest.