i can’t change my nickname in my game center

I tried the steps in that link (Use Game Center to play with friends - Apple Support) but my Game Center Nickname just keeps auto-populating with my old name. I type in a new name, I even tried using one of the suggested ones on my iPhone (just to check with names I knew for sure are available), and no matter what I do, as soon as I tap out of the Nickname field, the Nickname field re-populates with my old nickname.

iPhone 13, iOS16

Is anyone else experiencing this?

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