Whatever happened to full disclosure? So, it's not the standard situation of two parents making a person, it's more. So put on the birth certificate all the people that contributed to the creation of this child. Egg contributor and gestational mother are relevant here and should be included.
This is a case how the term biological mother is not what it was. In the old days the biological mother contributed the egg and carried the fetus for nine months. Technology now allows the role of biological mother to be split so she does not have all the jobs she used to do. So the definition of a biological mother has now changed and gestational mother does mean something.
One could guess the gestational mother in this case doesn't want the possible future trouble/hassle of adoption issues as she was doing the guys a favour and wants to be like the anonymous donor of the egg. Because if the donor can be anonymous, she figures, she can be anonymous too. So, I don't think the egg donor should be anonymous either.