Legal Question in Family Law in California

Yes you can add the father's name to the birth certificate, but "on the birth certificate" is an outdated notion. All legal relevance of parents names on birth certificates lost most legal relevance a few decades ago. All the name on the birth certificate is worth today is it creates a presumption of who the parents are, which can be overturned by proof otherwise. So there is no need to "add" the father "to the birth certificate."

What has to be done in order to ask CPS to turn over custody to him is the father has to establish legal paternity. That is done either by both parents signing a voluntary declaration of paternity, or by having the local child support agency (the CA Dept. of Child Support Services in most counties) file a paternity case for you if you also want to establish child support, or by filing a paternity case in superior court, the same as a woman does if she wants to prove a man is the father of her child. The cases can actually go both ways, and in fact a father coming forward to establish paternity and take responsibility for his child is favored by the courts. More information on how to establish paternity can be found here: http://www.courts.ca.gov/1201.htm

The father should also notify the CPS office that he is doing this and coordinate with them to make sure he is doing everything they expect and need him to do in order to qualify to take custody once he is proved to be the legal father. If he is well suited to care for the child they may also help the process along.