See tip 475 for information on renaiming a domain.

The steps for renaming a Primary Domain Controller (PDC) vs a Backup Domain Computer (BDC) are different.

To rename a PDC:
1. Control Panel / Network / Identification. Click the Change button and type the new computer name. Reboot.
2. Server Manager / Add to Domain, add the new name as a BDC (it will actually be added as a PDC).
3. Server Manager / Remove from Domain, remove the old name and any duplicate new name entry as a BDC.

To rename a BDC:
1. Server Manager / Add to Domain, add the new name as a BDC.
2. Control Panel / Network / Identification. Click the Change button and type the new computer name. Reboot.
3. On the PDC, Server Manager, select the new BDC and Sync with Primary. Select old BDC and Remove from Domain