Here is why I think the name will not change.
I've been watching the Redskins since I was a kid in 1990 at the tail end of the Joe Gibbs dynasty teams, so I guess I'm right on the cusp of being old school. Until this season, I hadn't watched a single game for the last 10 years (The Dan Snyder effect). With him gone, it's as if a giant weight has been lifted off this franchise. There's hope again, and a lot of us old fans are returning.
Maybe I'm in the minority as a somewhat old school fan, but I could care less about the name of the team. I never felt fully comfortable with the name Redskins and I'm not sad that it's gone. I understand that there's a lot of history under the old name, but I feel like the name was too problematic to keep. I do, however, miss the old logo and I hope it makes a comeback as an alternate jersey.
At first I thought the name Commanders was kind of lame, but I've gotten used to it and it doesn't bother me anymore. If there were enough fans who really hated the name, the team would change it again. The problem is that most of the fans who hate the name, will only be happy if it goes back to Redskins, which is a pipe dream, so it doesn't really matter what they think. They are deluding themselves if they think the old name and all of it's problems are coming back.
Without those old school "change it back to Redskins" fans, that only leaves the fans who hate the name Commanders, but don't want it to go back to being the Redskins. That's not a big enough portion of the fan base to inspire the team to make a change. The majority of Washington Fans, are made up of either old school people like me who don't want to go back to the old name or don't really care, and younger fans who weren't around for the glory days and are just fine with the name Commanders.
My final thoughts. Redskins was never a great name, but because of the history of the franchise with it's hall of fame players and championships, it came to have special meaning to us fans. I don't think the name Commanders is a great name either, but under promising new ownership and a young generational Quarterback, maybe they can make some history of their own, and we'll come to feel differently about the name Commanders in a few decades.