I was told f2pers can't change their display name. If I am a member with a display name and I become a nonmember, do I lose that display name?

No. (as far as I know)

No

No.

 

If you change your name while you are a member the effect wills carry on when you revert back to a F2p

They don't revert back to the original. If they did, that would cause a lot of conflicts within the game engine (other people can change to your previous displayname).

 

Also you can change your user with Funorb membership in case you didn't know.