Option 1:

To edit your child's player name, press the Home Button with the Higher Volume button to enter the Parent Settings Menu. Select the Manage Profiles option. Select the name of the Profile you wish to change.

Use the keyboard to edit the name of the profile and press the green button with the checkmark to save your changes.  After you return to the edit profile screen, press the green checkmark to save this change.

Option 2:

From the Home Screen, tap on the child’s name or picture at the top of the screen.

This will bring up the “About Me” Screen. Look for the button with a pencil.
This will launch the Edit Profile screen.
Tap on the name and this will bring up the edit name option (keyboard appears).
After you edit the name, press the green check mark.  
After you return to the edit profile screen, press the green checkmark to save this change.