The domain name is part of the server name! Open up SQL Server, SSMS, expand security for the server and look at the users. Notice the Windows users are OldDomain\UserName? It never changed.
Also do a SELECT @@SERVERNAME. Notice it'll reference the old domain name.
Internally, SQL Server doesn't know the server changed domains and thus has a different 'fully qualified host name'.
Please do the following:
-Rename it with the correct name if it showed up as the old domain following these instructions.
-Make sure you have admin rights to the machine, and add the new domain users mirroring permissions off the old one.
Those would be the main steps needed to ensure a smooth domain rename. Clustering is even more sensitive to it.