In order to update the name on a Vermont ID, the applicant must first change their name with the Social Security Administration, then submit a court order certifying the name change. The Vermont Department of Motor Vehicles addresses name change here. Applicants must notify the DMV of a legal name change within 30 days of the name change.
No documentation is needed to update the gender to M, F, or X on a Vermont ID. The DMV has information on their website clarifying that gender is a self-designated descriptor. If applying for a Vermont license for the first time, fill out the Driver's License Application and select the appropriate gender marker. If applying for a corrected license, fill out the Replacement License Application with the appropriate gender marker selected.