WHICH RULES DO I FOLLOW?
Every state has its own processes for name changes and its own options and rules for gender marker changes.
It's often hard to figure out which rules apply to you, especially if you no longer live in the same state you were born in.
Name Change
You change your legal name based on the rules in the county and state you currently reside* in.
You always change your legal name through a judge at a courthouse.
Once you go through your current county courthouse to change your name, you will need to mail a copy of your certified judgment/order to the state that you were BORN IN, so they can update your birth records and send you a new birth certificate.
Gender Marker Change
You change the gender marker on your state ID or Drivers License based on the rules of the state you currently reside* in.
You change the gender marker on your Birth Certificate based on the rules of the state you were BORN IN.
If you were born in Illinois, regardless of where you live now, you can change your IL Birth Certificate by mailing a simple notarized form to an office in Springfield, IL.
You DO NOT need a doctor or therapist to sign or send anything to change the GM on your IL Birth Certificate.
If you were born in Missouri, regardless of where you live now, you will need a court order from a judge to change your Missouri Birth Certificate.
This means that you will have to file a civil case in the county/state where you currently reside (even outside of Missouri), and ask a judge to sign a judgment stating that your "sex has been changed by surgical procedure" and all of your "legal documents should be amended to reflect that your new sex is male/female". Then you should send a certified copy to Jefferson City, Missouri.
*Legal Residence
*The county/state that you "reside" in is not always clear, especially for college students and people who are not stably housed. It's usually ok to go with your best guess based upon your own situation, as long as you try to be consistent.