Family name addition

This is regarding the addition of a family name from our generation. We are from Tamil Nadu so we havent had a family name until now. However my husband wants to add a family name and drop his father's initials henceforth. We were living in the UK until last year. Our son was born there and his birth certificate has been registered with this family name. what is the right way to add a family name and drop initials?

Thanks!