First, I did not change my name. My name has always been Schuyler. I only changed my gender marker. This can make things a bit faster and easier. In fact, if you are looking for the fastest way to correct your gender identity on official documents, you may want to consider just changing your gender marker first.
Second, I was born in New York, which has some of the most trans*-friendly rules for changing birth certificates, so your experience and procedures will be different if you are in a different state.
Rules and procedures for changing your name, ID and birth certificate vary by state, country and organization, so I have included links to resources that can give you specific information for your location at the end of this post.
Since I was only changing my gender markers, and I was born in a state that allows the correction of gender markers on a birth certificate, the only document I needed was a letter from my physician that attested to the fact that I have transitioned. For NY State and the US Passport office, the letter does not have to include any specifics about surgery or any other treatment methods. The letter I used was from Dr. Charles Garramone – who did my top surgery. Here are examples from TLDEF from the US Dept of State.
I then changed the rest of my documents over the course of about six months, which included my passport, global entry, driver’s license, insurance, airlines, consumer accounts, etc.