Is it possible to get a refund of my registration fee if I change my name on my car registration?
Yes, Surrender your plates and request a transfer receipt.
Do you also know about the registry if plates are lost, destroyed or stolen? . Can you explain the steps for lost, stolen, or destroyed license plates?
Yes. First report about the plates and  state the reason for the report. Next, you would need to surrender the registration. You will then be issued with a new registration and plates.