Different states have different requirements to obtain a court order name and/or gender marker change.
Usually to change your name only, no physician letter is required. Contact the county court house of the county in which you live and set up a court hearing date and complete any required forms for your hearing.
To change your gender marker, you will likely need an original physician's letter of support for your court hearing as well. The template letter attached complies with California law. To see what your state requires, check out the National Center for Transgender Equality's Interactive Map, or contact your county court house.