You can change the name to something offensive and e-mail them saying you left the room for a second and your brother changed it. They will give you the option to change it immediatley when you login.
This method is not recommended for really rare names, and you should be online and watching your e-mail whilst doing this. You can contact them by going to rs homepage > help > customer support > billing > submit a billing query.
After you've done that (on the account which has the name you want to transfer) the name will be available right away. And you can change your other accounts name to that display name. (If your other account has the option to change display name)