Fascinating name. I wonder if it literally refers to a puncheon of rum (70 gallons) or if it is a play on "puncheon rum" which is a seriously over-strength type of rum (75% abv) distilled in the Caribbean since the 17thC. Just the sort of thing that could be smuggled in through the back door of a waterfront pub!
Factoid: I was talking to the vicar of St George's a few years back. Although it's known that Rebecca Rolfe (aka Pocahontas) was buried in the chancel on 21 March 1617, that church was destroyed by fire (IIRC). Anyhow, when the new one was built in 1731 all trace of her grave was lost. The vicar thought this a good thing, visiting tourists (particularly Americans) don't insist on seeing the grave and disrupting church life, they are content with Partridge's statue outside. Indeed, (quietly ...) many think that that is her grave marker!