How do I change my username on Minecraft PE?

From the main menu, tap Settings, then press Profile (under the General category). At the top of the page will be a name box. Tap it to edit your username.

If you have the account linked to your Xbox account, you can go to the Xbox website to change your GamerTag which will in turn change your Minecraft PE Username as well

When on the title screen;

1. Click settings
2. Click profile
3. Change your name
4. If you are connected to xbkx live, you will have to disconnect first or change your gamer tag which costs money.

Visit https://www.xbox.com/ and login to your account:

Click again on the account icon and select XBOX profile:

Then edit your profile and change your gamer tag:

Finally you maybe need to restart / re-login in the game to see your new username.