1. First, make sure your legal name is the name you want on your ID. Here is the information about how to apply for a legal name change: http://www.vs.gov.bc.ca/name/howto.html Here is the form for applying for a legal name change. http://www.vs.gov.bc.ca/forms/vsa529.pdf
2. Then apply for a Change of Gender Designation on your birth certificate. There is a form that a physician or psychologist needs to sign to confirm your gender. Include that with your application.
Here are the application forms as well as the form for your doctor to sign.
3. Use the same form that your physician or psychologist signed and take it to ICBC and get a new driver's license and care card with the proper name and gender marker.