That appears to be quite similar to the patronymic pattern used in old Scotland and Wales, where “of <father’s name>” was typically appended to the child’s (usually just first) name to identify the family.
Perhaps this community were recent transplants from Wales or Scotland, and that’s how they identified themselves to the census taker? The census taker may have made a decision to record the names as he was told, rather than be put in the position of having to “reformulate” them.
I’d be curious to see how this community was enumerated in the 1830 and/or the 1810 census, to see if it was resolved in those instances.