wuethrich I see... really big problem. The Flarum user system (or maybe just username) must be rebuilt to give more flexibility. Even because Display Names are pretty important in some communities (more in my case - I run a Social Network).
To change the email is pretty simple, it is enough to do a REST API request and that's all... the main problem is the username.
I think, since this is not a fault of your ext, maybe it is better to post on meta. When I have some spare time will create a post there with some ideas and explain the problem here.
Thank you, anyway; your extension is great even because doesn't use any of the other "complicated" methods like oAuth or SAML. It's pretty genious.