Are you wanting to transfer the remaining registration credit to another vehicle that you need to register?
I wasn't wanting to transfer the credit that way.  I was not aware that I could, but, since you said that it is possible to transfer the remaining registration credit to another vehicle, I might wait as I am about to purchase my husband a new car.
When you surrender your vehicle plates to the DMV, you may be eligible to transfer the remaining registration credit to another vehicle you want to register, or get a refund for the registration fee.  You get a refund or registration transfer credit for your vehicle plate fee, title certificate fee and any other fee or tax that you paid when you registered the vehicle.
Will I get this refund immediately when I surrender my plates?
When you surrender your plates, your Receipt FS-6 T indicates if you are eligible to receive a refund.  If you are eligible and you do not request a transfer receipt, the refund will be processed automatically and you will receive it in the mail in several weeks.
What was the form that would indicate if I am eligible for the refund?
Your Receipt FS-6 T indicates if you are eligible to receive a refund.
How do I apply for a full 2-year refund if my registration was never used?
You can apply for a refund of the 2-year registration fee only if the registration was truly never used and it is not more than 60 days from the date the registration was issued.  A processing fee of a dollar is subtracted from the refund amount.  To apply, you must surrender the vehicle plates and the unused registration sticker and stub at the DMV office and request a 2-year refund.  If you are eligible, the DMV will issue a receipt that displays two year refund.
What procedure to I have to follow to get this refund, though, if I have changed my name?
You must still surrender the vehicle plates at a DMV office, but request a transfer receipt, not a refund receipt.  You will then send that to the address of the Request for Refund MV-215 form along with the completed and signed Request for Refund [1] MV-215 and proof of the name change such as a marriage certificate, divorce certificate, or other court papers.   At that point, the DMV will issue your refund in your new name if you are eligible.
Will the DMV issue a refund if the registrant died?