Here`s one way to get rid of the minor irritation. Go to User Accounts and name a new one of your own. (You can`t have it the same name as your current - so rename that one first if necessary) Log Off and log back in with your new User Account. Log off and reboot.
Log in under the "old" account. Then go to Control Panel>Files & Transfer Wizard and save the file to your hard disc in c:\Transfer. Reboot and log in as your new user account, run the file and settings transfer wizard again "importing" the file from c:\transfer. You have now created an identical account. Once you are sure that everything runs as it did before, say a week or so, go to user accounts and delete the original account. (Take the option to delete files) Then delete the folder c:\transfer.
The default name you wan`t to remove is only there because it is the only user account on the computer other than administrator and all users. (Plus possibly guest account) By default XP needs at least one named account.