Brian, I think it depends on the vicar of the parish at the time (and which parish) as to whether more information is entered in the baptism record than on the official registered birth form. After all, he often knew the couple, unlike the Registrar.
However, if both parents were given, as was often the case in Maughold, and sometimes with extra identifying details of the father, their names should both be shown on the IGI (indexed under the mother's surname, even when the father's name was given first on the baptism record).

Sue