If you're not willing to walk up to a Native American and call him a redskin, then you really have no rational argument in favor of Washington retaining this name. You can appeal to tradition, and you can dig up some random Native American that isn't offended by the name. But the simple fact is most Natives would not want to hear this word used to describe them, and that's the only thing that matters.
As recently noted, I've switched from anti-name change to pro-name change, so I'm on the name change side, but this is one argument I don't really agree with...perhaps it's splitting hairs, but I don't think any of us would go up to ANYONE of another race, and feel comfortable calling them by their
race (even agreed-upon unoffensive racial names). You don't greet/introduce people by their race (irregardless of whether the term you use is a nickname, slur, or socially accepted descriptor).
Case in point, would you go up to Ndamukong Suh and say, "Hey there African American!" or would you refrain because you realize he'd probably be a bit offended by being referred to as a race and kick your ###? Likewise, would you introduce a friend by saying, "This is my good friend Xao. He's Asian."
You don't utilize a racial name when addressing people. Irregardless of whether the racial name is offensive or not. The practice itself is seen as offensive by most.