I am a St.John's University Alum, and back in 1994 St. John's changed their nickname from the Redmen to the Red Storm. While I don't like the Red Storm name, I understand the change now as I have gotten older. Siena changed their name, and I recall Syracuse changing a mascot back in 1978, 1979 or so from a Saltine Warrior. UMASS was also the Redmen too, they changed to the Minutemen.
So there is some precedent, especially at the college level.
I understand Dan Synder to a point here, the Redskins have a long standing tradition in Washington, that encompasses the city and its fans for many decades. And while most do not find the name offensive in any way, I bet most of those people that do not find it offensive, do not truly know what the term Redskins means. But I can sympathize with Native American culture if they do find this name offensive. And like someone posted earlier, many are not offended unless it goes after their culture.
I predict the Redskins will evantually change the name.