My feeling is that the woman who gave birth, should continue to be registered as the mother on the birth certificate and the father should be the biological father, but that he only needs to declare this to be true, or to be married to the mother, not requiring a DNA test or anything.
I think it should still be acceptable to have no father registered so that women who don’t know who the father is, or who were subjected to sexual violence etc, shouldn’t be forced to interact with her attacker.
Where donors are used, I believe there should be some sort of record at the registering of their birth, so the child and future generations can know their genetic heritage, but there should be two versions of a birth certificate so that this doesn’t have to be disclosed day to day when verifying that person’s identity.
I’m on the fence as to whether a person with no biological relationship to the child should be registered on the birth certificate in addition to the biological parents (birth mother and egg donor mother if not the same, and the biological father).