If you are over the age of 17, you may have a UK driver's licence, or a provisional driver's licence. You can update your name and gender on either of these - both follow a similar process. If you do not have one, but would like one, you will need to apply for a provisional licence.
A driving licence is a piece of identification with your name on it, as well as a picture of you, and your date of birth. It is often used as a proof of age, as well as proof of ability to drive. However, you do not need to own a vehicle, or have passed your test to own one.
To change your name on your driving licence, you will need a 'D1 - Application for a driving licence' if you drive a car or motorbike, or a 'D2 - Application for a lorry/bus licence' if you drive a lorry or a bus. You can order these forms here, or pick-up paper copies from the Post Office.
Forms should be completed and returned to the correct address. You'll also need to send a deed poll and your old driving licence. If you're changing your picture, you will also need to send an appropriate photograph of yourself.