The name isn't even originally Washington's, they started as the Boston Braves, then switched to Redskins when they moved to Fenway Park to mimic the Red Sox name.
My college changed from Warriors to Golden Eagles, who cares, I still root for them. The Bills could change to Bisons, Stampede, or Chicken Wings, who cares, I'd still allow myself to be disappointed by them. If you can avoid offending an ethnic group, then why not, the benefit outways the inconveinence. Just another example of some white people complaining that "those people" are trying to take "our country" away from us.