This happens when your acc has been both permanently banned and deleted. Happened to me a while back and for weeks I couldn't get a helpful reply from anyone on twitter, reddit or jagex support. I could successfully recover the account but no matter what the password I set it to wouldn't work. Eventually made a new account and asked on the RS forums and they confirmed that occasionally account names will be totally deleted when perm banned. The char still exists sort of, but the username is deleted and the account is banned, therefore you can successfully recover it over and over but will always get an invalid username/password reply. If you wanna be sure, check your recovery email. It'll say your account was recovered successfully but in place of the account name you may see "invalid" or "unknown." Also you can try to check it on the hiscores.
Edit: Yeah just reread your post and the fact that you mention it saying "Character name unavailable" confirms it. There's a chance it could just be a forced name change (e.g. your name was offensive and jagex removed it) and in that case try to log into the account settings section and create a new name. If you can't login to that, chances are it was either deleted by accident (really slim chance tbh) or you were perm banned and your user was taken with it.
Anyone know what happened to my account?
