It's not all that simple.
First, get your name to match you once you are full time. Just do it. You'll be less self-conscious.
Second, depending on state, you may be able to change your gender marker on certain documents. For example, here in Texas we can now get driver's license updated without surgery, just a court order.
Also, with a letter (I think from your therapist but maybe from your doctor, I have to go check to be sure), you can get a new US passport with correct gender and also update your Social Security records, all before surgery.
It's the birth certificates that cause the most issues for most people and those vary widely by state. Some refuse to allow any changes at all, like Ohio (so glad mom drove across the river to have me in Wheeling, West Virginia now!!). Others, like California, allow the birth certificate to be amended with just a letter. And most still require GRS (or SRS if you prefer that term).