You cannot delete the administrator ID. You can rename it or disable it. Note that renaming only changes the friendly name not the SID. Since you can still address it by the well known SID, there is not much gained by renaming the account.
If you are trying to harden the system disable the administrator account, create a new account and make it a member of the administrators group.
Personally, give the administrator account a good strong password, set a reasonable account lockout policy (10 tries, 15 minutes), audit login failures and monitor the logs.
Should you need to manage who has the local administrator password, there are several tools available to manage that process, will change the password after access and on set tiem intervals.
Hide a User from the Welcome Screen in Windows XP.