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If you are going to disable all notifications from Game Center, just tap on the option of "Notifications" in Settings, and choose Game Center to turn off its notifications.
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Then tap op the "Apple ID" in the top of Game Center page, and type with your Apple ID and passwords, then hit on the "Sign Out" option. To actually modify Game Center settings, launch Settings on the main screen of iPhone, scroll up and choose Game Center under iTunes U. thus, the only way to get rid of Game Center in iOS 9 and earlier device it to hide it when you are not able to delete Game Center: If you are running iOS 9 or earlier, it is unfortunately that you are not allowed to delete any apps preloaded on iOS 9 and earlier, including Game Center, iTunes Store, App Stores, Calculator, Clock and Stocks app and etc. This is because that Apple has ended the existence of Game Center as an individual app, so there is no Game Center at all in any iOS device running on iOS 10/10.1/10.2/10.3. If you are running iOS 10 on your device, you are lucky enough that you can get rid of Game Center without deleting it from your iPhone. Now you will find that all the features associated with Game Center are erased. Wait for a couple of seconds until the feature is disabled. In the "Game Center" page, tap on the toggle near Game Center and switch it from Green to White to remove Game Center on your iPhone.
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Launch Settings app on the home screen of iPhone, scroll down the page and tap on Game Center from the lists. Move to the bottom of the Game Center page, and tap “Sign Out” to disable the Game Center on iOS 14. Open Settings app on your iPhone or iPad, and scroll down to find and tap “Game Center”. If you are not interested in these features come with Game Center, follow the step-by-step instructions to delete your Game Center on iPhone: How to disable Game Center on iOS 14
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Game Center is developed by Apple, aimed at help you sync your game process data, achievement, and online multiplayer. Part 1: How to delete game center on iPhone
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