Everyone looking to change their PFP in Game Center, look here.
So I see it all the time where people can't figure out how to change their profile picture on the game center cause there isn't a button to do it and unfortunately you're right, there isn't a button.
You can do it however, and it's really really dumb and it has always been really dumb.
Apple needs to make this a little more simple.
This is a video of how it works and I'll give a description, but it's really dumb.
You literally need to click and drag a photo. That's it.
If you're on an iPhone or iPad, just grab the photo and switch back to the app and drop it in.
Seems simple but when no one tells you it's really annoying, especially when they SHOULD have made it just a simple "add photo" button. It's not that hard. Its a billion dollar company.