Found this at Wikipedia:
“Bread-and-butter pickles are a marinated pickle produced with sliced cucumbers in a solution of vinegar, sugar and spices which may be either be processed by canning or simply chilled as refrigerator pickles. The origin of the name and the spread of their popularity in the United States is attributed to Omar and Cora Fanning, a pair of Illinois cucumber farmers who started selling sweet and sour pickles in the 1920s and filed for the trademark “Fanning’s Bread and Butter Pickles” in 1923 (though the recipe and similar ones are probably much older). The story attached to the name is that the Fannings survived rough years by making the pickles with their surplus of undersized cucumbers and bartering them with their grocer for staples such as bread and butter.”
I don’t know how true it is.