I would try to re clone the LC. However during the process at the "Guest Customization" window select "Customize using the Customization Wizard" and check "Power on this virtual..."
Enter in your domain info you want to utilize as if you where installing the OS a new, but be sure to check "Generate New Security ID" when you get to "Operating System Options".
That should at a minimum get you a new SID which will be associated with the new name while leaving it a member of the domain.
Just a thought.
-Tanner