Helpfully, the mother's maiden name was included.
Also, both parents' names were given in Latin. And of course, not everyone knows that the Latin version of William is Guilelmus. In cases where this is the father's name, such baptisms may remain unnoticed - hiding in plain sight, as it were. The first baptism in CofE would put you off the scent, especially when there is no family knowledge of a Catholic connection.
UKgirl