Calling children by the mother's surname in the IGI appears to contradict what happened in the IOM. Whether or not the parents later married, the child seemed to be almost always called by the paternal surname when the father's name was given at baptism.
For example, the child called Charles Christian in the IGI [Charles illegitimate son of Chas Joughin & Margt Christian] was called Charles Joughin in his Christian grandmother's will, when he married, other PRs, and in census returns.
In wills illegitimate children whose parents haven't married are often mentioned by their father's surname [e.g. to sister Margt Dowan, to her son John Sayle].
So the IGI alone decided they were to be given the mother's surname. - Which makes them pretty difficult to find on the IGI.
Sue