I know the original post was a year old, but as a pilot who has gone through the process, my best advice is to expect A LOT OF TROUBLE.
Once you list gender dysphoria on your medical application, you trigger a cascade of issues. The application is automatically rejected and kicked to Oklahoma. From there it goes all over the place until it lands on the desk of the cheif FAA Psychologist where it will sit indefinitely. It took me getting Barbara Boxer (Senator-CA) involved to finally get them to move. I was grounded for four months for nothing more than treating my disorder.
This was all done with my old name. Eventually my medical certificate was all that was left with my old name. So I requested a name change. I got a request back for a proof of name change (keep in mind my pilot's license issued by the FAA already has the correct name). I sent in the court order and got back a request for a mental status assessment by my therapist (keep in mind, my medical certificate is valid, I just wanted a name change). I submitted that and got a request for a physical evaluation... Sigh it never ends.
