1762, said to be a reference to John Montagu (1718-1792), 4th Earl of Sandwich, who was said to be an inveterate gambler who ate slices of cold meat between bread at the gaming table during marathon sessions rather than rising for a proper meal (this account of the origin dates to 1770).
It also was in his honor that Cook named the Hawaiian islands (1778) when Montagu was first lord of the Admiralty (hence the occasional 19c. British Sandwicher for "a Hawaiian"). The family name is from the place in Kent, one of the Cinque Ports, Old English Sandwicæ, literally "sandy harbor (or trading center)." For pronunciation, see cabbage. Sandwich board, one before and one behind the carrier, is from 1864.