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 offensive or personally identifying content. If that is the case, please submit a ticket to the support staff.