The process for changing one’s name and gender on a birth certificate varies from state to state. Look at the laws of the state in which the birth certificate was issued. To learn about the requirements in your state, visit Lambda Legal’s Comprehensive List or The National Center for Transgender Equality's Interactive Map.
Usually, you will likely need to obtain a court order name and/or gender marker change first. For gender marker change, most states require that a health care provider fill out a form or write a letter.
In California, for name change and/or gender marker change, submit the court order, old birth certificate, and form VS-23 (for name change) or VS-24 (for gender marker change) to the CA Office of Vital Records, along with your payment. The gender category options are now male, female, or non-binary.