This is one of those areas where Irish practice deviated from English law.
In law, illegitimate children had no fathers. They were "fillius nullis", which means literally a child of nobody. Therefore civil registrations did not show alleged or reputed fathers, and only the mother's surname will appear.
However, Irish social practice, as in so many things, departed from the English legal prescription. The Irish practice - not universal, but the majority of the time in my opinion - was that an illegitimate child was indeed named for the reputed or alleged father. For this reason, a father's name often does appear on baptismal records - but not always, and remember that a baptismal name is the Christian name, not a surname.
That is very helpful, thanks. Am I misunderstanding this? Is the "alleged" father named (surname) anywhere on baptism records? If so, had the potential father no way of objecting to being named, even if he didn't think he was the father? Bet that caused some family feuds! Would it cause a mother to have her child baptised out of the area where she was known - where no questions might be asked?
My point is that civil registration and baptism had different rules/goals.
For civil registration, they did not want to know or record any alleged father's name, as legally there was no father. I have seen many a registration where the registrar either started to or had finished writing in the putative father's name, only to then strike it out on realizing that the birth was illegitimate.
For baptism, however, I think they wanted to know the fathers name - in my experience, the alleged father's name is there more often than not. And no, the alleged father had no way to know or object. Also, remember, baptism is a sacrament, there was and is a heavy obligation to tell the truth.
