In order to change your Player Name, click on the avatar icon in the top-left of the main screen. A screen will open showing your player name, mission progress, and power level. Tap on your player name(or the box that says "Enter Player Name", remove the "Enter Player Name" text, and type in the name you'd like to use.

Note that vulgar and inappropriate player names that go against Next Games' Fair Play Policy could result in a ban from the game, so choose your player name responsibly!