If a child does not 'have a mother' but has two fathers who are not married, who legally can register the birth????
A birth certificate records the circumstances of a birth, so the mother will always be on the birth certificate, even if a surrogate.
If she is married, her husband will be the defacto father. Even if these people have no genetic link to the child, in the absence of a court order they are the parents.
In the case of surrogate pregnancies, there is a mechanism for producing a new document later that includes the legal/genetic parents, but the original birth certificate will still exist as a record of birth.