Correct - verify first, change only what is actually wrong, and let Netlogon re-register its SPNs. On the renamed DC, check the current SPNs:
setspn -L NEWDC
Then search for stale SPNs containing the old name:
setspn -Q */OLDDC
setspn -Q */OLDDC.contoso.com
Also check for duplicate SPNs:
setspn -X
If you find an obsolete SPN registered against the renamed DC, remove only that specific entry:
setspn -D HOST/OLDDC NEWDC
If a required SPN is genuinely missing, use -S, which checks for duplicates before adding it:
setspn -S HOST/NEWDC NEWDC
setspn -S HOST/NEWDC.contoso.com NEWDC
Afterward, restart Netlogon to trigger registration again:
net stop netlogon
net start netlogon
Finally, verify replication with:
repadmin /replsummary
Do not delete and recreate the entire SPN set manually. Domain Controllers have numerous automatically managed SPNs, and unnecessary changes can create additional Kerberos problems.
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hth
Marcin