Hi
I am afraid that sometimes the minister got it wrong on the marriage certificate (my own experience in my husband's family) or people simply made up a name to avoid embarrassment if marrying rather more respectably (though again, in my experience there were loads of kids born 'out of wedlock' who went on to make good marriages and careers without any fathers) or it was what he was told and believed. Sometimes the name of the grandfather was put on or the name of the stepfather. (or even the mother!)
Have you found a baptism? Sometimes the clergy wrote comments in the margin about who the father might be. Or did Emma try to get any support from the father? That might be in court records
Fiona