I was under the impression that Baptisms usually had the maiden name of the mother. You need to check marriages as well. Whatever the situation the father has been acknowledged. I also picked up the idea from somewhere that on the IOM the child could choose later on to be known by the father's surname or the mother's surname in the case of illegitimacy.
One member of my IOM (Kermode)family was in such a situation. It had confused later generations who named one son born in Australia with his second name Kermode. Well the memory lingers on!
regs. Lorraine Daly.