They probably already told you this in their reply but I am going to add it for anyone else that sees this thread. When you use a third party login for FANDOM (which you can currently do with Google, Facebook, or Twitch), you are not copy-and-pasting your username and password from that third party. What is happening is that FANDOM is contacting the third party and asking them to handle the login. The third party verifies the username and password you give against the one they have for you and then tells FANDOM the login is legit. I would imagine that they probably do this by simply setting your password to some ungodly long random sequence that only the third party has access to; but that is just a guess. The point is, the "password" FANDOM expects for your account is not the one you use for Google or whatever third party you linked your FANDOM account to.
As you found, this causes issues when you want to do something like rename your account. You certainly are not the first person to have this problem. In fact, this is another recent instance. In this case, the user was able to figure it out on their own. Essentially, you need to unlink your account and then reset your FANDOM password to something you know.
That is the way I feel and also why I don't use a password manager (effectively the same thing). There are definitely a few stories out there where this has been an issue (i.e. Firefox forcefully disabling "questionable" add-ins, some of them password managers). However, there is quite a point to be made about improved security. As long as you go with a reliable entity, you will probably be fine.