The paper the Notary Public signed could have said the father's name was "Rainbow Brite" and the notary wouldn't need to care or even look for it. The notary is there ONLY to witness the signature and identification of the person whose name is being notarized. As long as the notary watches that person (in this case the mother) sign the document in his/her presence, the document does not have to be verified for anything more than the proper signature.