Can I log out of my Game Center account and log in with another one but still stay logged into my main Apple ID for everything else other than Game Center?

Hey there JurassicSaver,

Thanks so much for using Apple Support Communities.

You should definitely be able to sign in to Game Center using a different Apple ID than the one you use for iCloud and the rest of your Apple ID related content. It looks like you're on iPadOS, so we'll share the steps for that below but if you need them for any other device, you can find everything you'll need right here: Use Game Center to play with friends - Apple Support

To sign in to Game Center on your iPad:

Set up your Game Center profile

1. Go to Settings  > Game Center, then sign in with your Apple ID.

2. Do any of the following:

* Choose a nickname: Tap Nickname, then enter a name or choose one of the suggestions. Your friends see your nickname when you play games together.

* Personalize your avatar: Tap Edit Avatar, then create a new Memoji, use an existing Memoji, or customize how your initials appear.

To view your Game Center profile, achievements, recent games, friends, and their activity, go to Settings > Game Center > [your profile].

We hope this does the trick for you!

Cheers.