Can a father legally take a child if he is not on the birth certificate?

My friend wants to give her daughter the last name of her father but doesnt want him listed on the birth certifcate. We live in California can she legally just give the baby any name with out the father being on...

If the father is listed on the birth certificate- do they have to have custody awarded to one of the parents or is the mother the one who 'automatically' has established custody?

My daughter got pregnaunt and it was between two men. The one man decided to sign birth certificate knowing that he may or may not be the father. They ended up getting married and now they are getting a divorce....

When i had my child i did not put the father on the birth certificate at the time but i am trying to get child support from the father now how does this effect child support?

He had went to court with the woman to figure out the child support and asked for a paternity test. this woman stated that she wanted to drop all requests for child support. He was wondering how to get the ball...