
Quoting
Adding the Father's Name to the Certificate:
As of 1/1/1997, California State Law permits the father's name to be reported on the birth certificate only if the couple is legally married or if, by signing a Declaration of Paternity form, the father agrees to give up his legal rights to challenge paternity. The form is available at birthing hospitals, pre-natal clinics, the Department of Child Support Services, the Family Support Bureau of the San Francisco District Attorney's Office, our office at 101 Grove St, Room #113, San Francisco, CA, and the office of any local California Registrar of Births.