If the Navajo Nation had enough people and money to have its own NFL team, it could name it the Redskins if it wanted.
Actually, the Navajo call themselves the Diné, not Redskins.
Also, if the Redskins were called the Indians, or the name of a particular tribe, rather than a racial slur, there would be much less controversy.
I think that's more problematic. Cleveland already gets its share of grief, partly for the same reason as the Washington Redskins, but also because the indigenous people of the Americas know that Indians are from India. Also, the using the word Indians merely propagates the errors of Columbus and his cartographers, who thought that the Antilles were in the East Indies.