To change your gender marker on an ID:
Form 4214-LAM License Amendments Proof Of Sex Change In order to amend a driver license to reflect a sex change, a statement from the physician, psychologist or psychiatrist must accompany the request. The statement must be on their letterhead and must certify the one gender predominates over the other and the licensee in question is either a male or female. Staple the statement to the Application for Driver license, Form MV-44.
For getting your info changed on your ID in NY you just need a doctor's letter saying you identify as such and such thing or are undergoing treatment tho change your sex.