Don’t be too grossed out when you hear this name; it doesn’t mean “butt” as in “rear end” - the cut actually comes from the front shoulder of the pig.
During colonial days New England butchers tended to take less prized cuts of pork like these and pack them into barrels for storage and transport. The barrels the pork went into were called butts. This particular shoulder cut became known around the country as a New England specialty, and hence it became the “Boston butt.” Interesting that this name is not used in Boston. A hogshead is 64.8 US gallons and butt it equal to two US hogsheads or 126 US gallons.