President Harry S. Truman's middle initial 'S' is itself his middle name; the initial does not stand for anything. Apparently, Truman's parents were torn over whether to give their son a middle name in tribute to his maternal grandfather, Solomon Young, or his paternal grandfather, Anderson Shipp Truman, with Mr. and Mrs. Truman settling on the compromise of the single initial S. The practice of giving a child a single initial in place of a full name is an accepted convention in the Scotch-Irish tradition, and this practice can even be applied to a child's first name.
Though official stationery and President Truman's own written signature included the use of a period after the middle initial 'S,' indicating that the letter is an abbreviation, this practice does not actually indicate that the initial is a shortened version of a longer name. According to the Truman Presidential Library, Truman himself told reporters in 1962 that the period after his middle initial should be omitted (in spite of the fact that he himself used it) because the letter did not actually stand for anything. However, he likely said this in jest, and style guides also support the use of a period after a middle initial that does not actually stand for anything.