Changing nickname in Pokemon Go became available due to the recent update on August 8, 2016. A player can rename his avatar's name only once. The following shows how to change nickname.
How to rename an avatar
1. Tap Pokeball-shaped icon
Tap the icon at the bottom of the map view screen. The main menu pops up after tapping the icon.
2. Tap settings icon
Tap the settings icon at the top right corner of the screen to open the settings menu.
3. 'Change Nickname' on the menu
A new tab, 'Change Nickname' is added on the settings menu. To change your nick name in Pokemon Go, tap the menu.
4. Tap 'YES' for renaming
You will be asked to make sure. If you want to change nickname, tap 'YES'.
Note: A player is allowed to change nickname only once!!
5. Enter the nickname
Now you can make the nickname you want to use in Pokemon Go. Again, changing the nickname is available only one time.