I'm not sure about DMV. All I have read says that DMV wants a letter from a therapist, so an MD wouldn't be able to write that either. That doesn't sound true to me, so I'm just going to see when I get there. I'm getting a court order name and sex change from Multnomah county first and, yes, my ND did write me a letter for that.
You should be able to tell your new doctor where you previously had labs done and they can call to have the results sent over. As long as it was within a year, or whatever timeline the doctor finds appropriate.