With Pokemon Go vision 0.33.0 , it is now possible to change your trainer nickname, but Niantic labs only allow a single change per account. So you have to be sure about your desired nickname.
If you’re using an Android device,
Here is how you can change your nickname in Pokemon Go
1. Opens Pokemon Go either from your app drawer or home screen.
2. At the bottom of your home screen you should see a red poke ball; Tap on it
3. Tap on the settings button on the top right of your phone screen.
4. In the settings list, click on change nickname
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5. You would be asked “Do you want to change your nickname?” Tap YES
6. A space will be provided; there you are required to input your desired nickname
7. Tap OK and Yes to confirm
If you’ve confirmed this, your trainer’s nickname is changed forever. The only way you can choose a new nickname is by creating a new account.