According to Apple, you should not identify your users unless you have a good reason to do so.
As @Marat said that you are looking for a UUID, but keep in mind that this value may change (for example, if the user uninstalls your application and does not have any of your other applications).
A possible solution would be to store the UUID value in the keychain, and this way you will always use the same value.
Edit: Since your application is a game, you can use the Apple GameCenter . This will determine the users for you.
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