According to T.V.H. Fitzhugh's "Dictionary of Genealogy" If a child was born out of wedlock the the father's name was generally omitted; but after 1875 if the father accompanied the mother to the registrar's office and claimed paternity he could have his name entered on the certificate. So, unless he went with your Gt. Grandmother to register the birth his name would not appear.
A further thought occurs to me - if at all possible it might well be worth trying to get a look at the baptism register as the father's name may well have been entered by the priest. I know that getting sight of Catholic Baptism registers is sometimes difficult as they tend not to be lodged in the local record office but remain in the care of the original church; but - technically speaking - I am assured that they are public documents and an appeal to the relevant priest might well give you the information/confirmation that you seek.
jds1949