He wields a large, spiked club. His name may not be Jack as other Yorkshire folklore refers to "Jack in the Green" and more so the name Jack may just be a term for calling the person an unknown male, like John Doe today.
The figure in question carries a large, spiked club. It's possible that his name is not actually "Jack," but rather a colloquialism used to refer to an unknown male, similar to how one might say "the guy" or "the man."