The given name Bredine is found over 300 times in the 1865 Norwegian census so the name was not unique. It appears most commonly in the areas of southeast Norway.
The child might have been called Bredine to honor a female ancestor, an aunt, a friend, a neighbor or just because the parents liked the name.
In the rural areas of Norway at that time it would have been the most common practice to name children as was explained in the articles about Norwegian naming -- but there are always exceptions to any 'rule'. The more urban areas and those locations with frequent interchange with non-patronymic naming countries tended to wander from the traditional naming patterns first.