There are a system of caves in Somerset between Glastonbury and Bristol, known as Wookey Hole. Given that one of the founders was from Devon (immediately south of Somerset), perhaps that's where they got he name from.
Good call! Found this on their site:
The origins of the name Wookey Jack are uncertain. Some say that it’s related to Brynildson’s favorite band, Phish. Co-proprietor and British expatriate David Walker suggests a connection to Wookey Hole, an English village noted for its dark caves and resident witch.