Legal Question in Family Law in California

You cannot change a birth certificate, although you can change a name and in certain cases have a new birth certificate issued. If the named father does not object to the name change, you don't need any evidence of anything to change the child's name. If it is contested, then you have a court adjudication no matter what, and may as well have it be a full judgment of paternity if you are going to go to all that trouble. There are also other very important reasons, including such things as medical decision rights if you and your son were both injured in an accident and you were unconscious, for example, inheritance rights, public benefit rights such as social security, etc., that the true father should be determined and adjudicated, rather than just changing the name. You really should consult a local family law attorney to go over your options. If you are going to bother with genetic testing, you almost certainly should get a proper order of paternity.