This is a short tutorial on the steps required to change the display name in iPhone 4S Game Center.
Step 1: Press the menu button on iPhone 4S then tap the Game Center icon displayed in the Home Screen.
Step 2: Now your display name or the Game Center nickname will be displayed on the Screen. You can edit this name by clicking the Account information.
Step 3: This would display the following pop up screen with the option to View Account.
Step 4: Tapping the View Account will display the Account details screen. Scroll down the Account details screen and provide your desired name for Nickname.
Step 5: Then tap the Done button on the navigation bar after the making the required changes.