Changing your in-game display name is easy!
DC Legends uses the same information as your Game Center account, so you can update your name right from the Game Center page on your device.
To do this, simply go into your device's Settings Menu and locate the "Game Center" header, then tap on "Game Center Profile". Enter your new name, and tap "Done." You will see your new display name the next time you load into the game!
For general information regarding Game Center, please use this link