Using the Father's Surname without the Father's Proof of Acknowledgement

My Father was born in the year 1950 and his birth certificate was not NSO certified. We are trying to process his birth certificate but we are having problem with his surname because he is an illegitimate child and he is using his father's surname without acknowledgement. He has no proof of acknowledgement from his father because he was already dead but the wife of his father and their family acknowledged him. Can he still use his father's surname without the acknowledgement from the father? We are not after the inheritance or anything from them. We just need it to process his birth certificate. Please help us and advise on how to proceed. I would really appreciate any response because we don't know where to start.