not real father acknowledged on birth certificate, is it possible to change to the real father the family name of the child

not real father acknowledged on birth certificate, is it possible to change to the real father the family name of the child, ganito po kasi yon i have a boyfriend foriegner nabuntis po ako tapos umuwi siya sa canada pero alam nya nabuntis ako, tapos habang buntis ako nagkaroon ako ng live in partner pinoy ,cya ang nagacknowledge sa birth certficate, tapos ngayon yung foriegner gusto rin niya na i acknowlege sa birth ,pero hiwalay na kami ng live in partner ko na pinoy bumalik ako ngayon sa foriegner ever since po ang sinosuporta sa bata yumg foriegner , ano po ang gagawin ko, pls help me

Let the father file the petition to transfer the surname of his child to his. He may need to produce a DNA test to claim the child.