Please keep in mind that Best Fiends currently does not support saving multiple games on one device. Signing into multiple accounts with Best Fiends games saved on them may result in progress loss.
We strongly advise against allowing other players to sign into their Best Fiends accounts on your device or signing into your own Best Fiends connected account on another player's device.
However, if you have accidentally signed into an account you don't want to use for your game, here are the instructions on how to switch the currently active accounts.
Your Facebook account should be detected automatically and will match the same account you're using on your device in your Facebook app or browser. It should be enough to sign out of Facebook in the game (by accessing game's Menu > My Account > Disconnect), make sure that the correct account is active in your Facebook App/browser and try signing in again in your game (Menu > My Account > Sign in).
If those steps didn't help, please sign out of the current Facebook in your game and open the browser (or browsers if you use more than one) on your device and go to facebook.com. Please sign out of the Facebook account active there. If you're using a Facebook app, sign out of it as well.
Once this is done, open the game and try signing into a Facebook account. It should ask you to insert your Facebook login information which means you can select whichever account you need.
If you want to know more about how to manage apps using your Apple ID, disable your Apple ID sign in for an app (sign out of your Apple ID in an app) or adjust permissions, please take a look at this Support Article by Apple.