He has to change his name twice. Jagex implemented this system so that just in case you got hacked & the hacker changed your name, you could get it back.
Heres how your friend should do it.
He has his account with the rare name, he gets a bond on it, and changes his name to an offensive name like "bl0wmyC0kk". He joins a Jmod's friendschat and gets reported, then his name gets changed to something like "#23Jn32123H". At that point, you can grab his "Rare" name.