You can use netdom to rename any computer, including a domain controller:
netdom computername <old fqdn> /add:<new fqdn>
netdom computername <old fqdn> /makeprimary:<new fqdn>
netdom computername <new fqdn> /remove:<old fqdn>
However this will leave the attribute
msDS-AdditionalDnsHostName with the old name. Check this in ADUC attribute editor (or ADSIEDIT.msc):
Remove the old name and restart.
PS. This fixes not being able to re-use the old name on another computer. You get the error
The operation failed because SPN value provided for addition/modification is not unique forest-wide, and you will see the old domain name when you run
setspn -l <oldname>. Performing the above attribute changes fixes this.