Children abandoned by their father and his rights

I am an American Citizen that plans to marry a Philippines Citizen that has never been married. She has 2 children that were abandoned by their father after the birth of their 5-year-old daughter. He has not seen or provided for his children since. I want to marry the mother and bring her and the children to the USA. The older 7-year-old does not have his surname on his birth certificate. He has the maternal grandfather's surname who is now deceased. The 5-year-old has her father's surname. What do we need to do to change both of the children's sir name to their mother's sir name so she can bring them to live with us in the States?