Please note that it's currently not possible to purchase a name change in Battlerite Royale.
A name change can be purchased for 750 Gems in the original Battlerite only, you can access the option to change your username in the Collection menu, in the last option of the left column.
You have the same username in the original Battlerite and in Battlerite Royale, therefore if you change your username in one game, it will change in the other as well.
A name change costs 750 Gems. An exception can be made if your username contains personal information that could allow for identification outside of the game, such as your full name or email address. If that is the case, please submit a ticket to the support staff. Please note that confirmation of your identity may be requested.