I thought I would chip in a similar occurence in my genelogy work which I stumbled over last week.
It appears that my 2xgreat grandfather's first wife had her first child with another man to whom she was not married.
The birth records in the church for that child clearly state the name of the father, and there are no records of their having been married. In addition we can be quite sure that he was very much her senior at the time of conception. He already had 5 children by his wife and one of their daughter appears to be the age of my 2xgreat grandfather's first wife - perhaps they were even friends? We can be quite sure about this situation because the names of the people involved (particularly the bioligical father) at the time are quite unique lending to a high degree of confidence.
I was quite surprised as I was digging to see that the mother did reference the fathers name due to the out of wedlock situation. I thought how unusual - wouldn't there be shame in her listing the father in the church records? But with the clear open visibility of the father in church records I decided to re-think that maybe it wasn't considered a "shun" worthy event, rather just something that would happen and the job of the family and the church is to love and support all children.
To the other poster's note about the surname...as a point of reference, that child did maintain the last name of the mother "Larsen", the child neither took the name of the biological father nor the name of my 2x great grandfather who appears to have raised her.
Just thought I'd share as I stumbled on this last week and here you had posted recently too!!