This is a very common situation, and when we research our family histories, all we have to go on is the information from our relatives and the documents they created.
There is never any certainty that the fathers name included on any birth certificate is the cottect biological one anyway.
Is it possible that there is a family member that may have a clue to the identity of the missing father? Sometimes this infotmation comes to light in later years, for instance, when your maternal grandmother married, he father's name would have been put on her marriage cerrttyificate if she knew who it was, who brought the children up? Did the mother cope on her own or did she later marry and that man brought her up?
It may well be that the father and mother lived as man and wife anyway, in which case the father and mother should be buried together (more often than not).
It is good to try to think of reasons that the father's name is missing on the certificate, and the main one at that time was because the parents were not married and therefore the mother could not add the father at the time of registration for legal reasons, and more than likely, because of the fees, she only paid enough to register and get the free short certificate as legal proof she had registered the child, and these did not contain parental details. It was not often that the full copy was paid for at that time.
Were there any other children, siblings of your maternal grandmother, who may have a father's name added. What surnames are associated with the children or family that seem to be out of place?
There probably will never be a way of confirming the biological father with 100% accuracy unless any family story copmes to light that explains her mother's relationship with the father.