Above is a portrait of John Montagu, the fourth Earl of Sandwich. He seems to have been in good mood when he sat for the painting, perhaps this is because he knew his name would forever after be associated with one the greatest creations in the history of food.
According to the BBC the Earl asked for the particular serving so that he could eat while continuing to play cards and his friends asked "to have the same as Sandwich". The first written record of the sandwich was in 1762 and the Kent town of Sandwich, which is the earldom of the Montagu family, is celebrating the 250th anniversary of the meal.
It is fortunate that Sir Edward Montagu, a prominent naval commander, who became the first Earl of Sandwich when he was offered a peerage in 1660.
Sandwich not Portsmouth. Apparently Sir Edward Montagu chose the title because "at the time Sandwich was the premier sea port in England" (Not sure if that would be the case but let's not ruin a good story). When he was offered the earldom he could have chosen Portsmouth but he chose Sandwich - today we could be eating a Portsmouth.