I did my name change first because it was a step I could take at that time (No Prerequisites). Getting a gender marker change would have required a letter from a doctor. I would have had to see a therapist, then get a letter for HRT, then do HRT for a while before I could get that letter (I later started HRT). OTOH, I could change my name with a few trips to the courthouse and a bunch of money ($400 Filing Fee, $75 for Fingerprints, $20 for a New License, $20 to Amend my Birth Certificate, $38 for copies of my Birth Certificates, Unknown Cost for Gas, $128 to take time off work, etc...)