Changing a Child's Name: Father Used False Name on Child's Birth Certificate

My question involves name change laws in the State of: California

Must a father use his legal name on a child's birth certificate? My child's father, 'Greg', was born to an unwed woman but a father's name is given. When 'Greg' attended school he was known by a third name (not mother or father). When 'Greg' was about 18 he began using his uncle's last name. I didn't find out all of this (plus a lot of other shady/criminal things) until I was pregnant with our child. When the baby was born I agreed to the use of a hypenated last name on the birth certificate since we weren't married.

Long story short 'Greg' is a Jeckyl/Hyde and Mr. Hyde is now in full swing. My child and I now live in fear even though we have a restraining order "protecting" us from the violence that he exhibited after the baby was born.

Along with all the other legal issues I'm pursuing I really would like to get that name off of my child's birth certificate. 'Greg' is the biological father but the name is meaningless, inaccurate, and probably a fraud. How can I get it changed?

Changing a Child's Name: Father Used False Name on Child's Birth Certificate