On a side note, please don't use domain admins for this.
Create a service account with least privilege to rename computers.
If I remember rightly, by default Account Operators and Domain admins have the Active Directory rights to do this on computer objects.
Account Operators still give far too many permissions for the task at hand though.
So you can delegate just permissions to rename computer accounts.
Two permissions are required. The domain account needs "Rename a Computer Account" permissions for the and you have to have an account that is a member of the local administrators account on the computer being renamed. Create a group with these rights and then create a service account specifically for renaming accounts and add it to this group.