Why would you allow users to change their display name? It's a forum, not social media.

Of course it's social media. The username and avatar is one's social identity on a forum. I think you have a very narrow experience with forums if you find it surprising that someone wants to change their username if you accept that they would also want to change their avatar.

Checkout Remarkbox, I generate them a random display name when they sign up and then allow them to change their display name later.

Regardless of the type of application, why would you not want a user to be able to change their display name?

If I was able to change my display name on hacker news, I think I would.