The problem with trying to get teams to change their name or their logo/mascot, at least in the USA, is hindered by a rather large hurdle, the US Constitution, in particular, the First Amendment (usually referred to as "1A") , which guarantees all Americans the right to Freedom of Speech and Freedom of Expression.
Now, while there are accepted limitation to 1A, for example, Judge Oliver Wendell Holmes' (often misquoted) assertion that 1A does not give someone the right to yell "fire" in a crowded theatre, as well as limitations on hate speech that incite racial violence, that limitation does not extend to limiting names of sports teams. In the appeal against the conviction of George Johnson in
Texas v. Johnson (1989) Justice William J. Brennan, Jr. wrote in the decision that
"if there is a bedrock principle underlying the First Amendment, it is that government may not prohibit the expression of an idea simply because society finds the idea offensive or disagreeable."
Essentially, neither the federal or state governments nor any local authority, will never be able to force or direct the Washington team management to change their name. They can make it difficult for them to use the name, but they simply cannot legally force them, that would be a violation of 1A, and no judge would rule against the team.
In any case, maybe they should change their name to this...
https://dl.dropboxusercontent.com/u/98915197/JREF/Redskins.png
"Paleskin" is a derogatory term used by
"Indians" to describe white people in old Western movies. It could be taken to be every bit as offensive by a small number of white people as
"Redskin" is by a small number of Native Americans. However, it won't be, it would be regarded as a LOL and many would see it as a slap on the face for the various SJW's out there driving for a change.