The S doesn't really stand for anything
John Anderson Truman, a mule trader and farmer, and Martha Ellen Truman welcomed their first child, Truman, on May 8, 1884, in Lamar, Missouri. Following some thought, John and Martha came to the conclusion that they couldn't decide on a middle name for their first kid, so they chose "S." His paternal grandfather's middle name was Shipp, whereas his maternal grandfather's was Solomon. His parents agreed to "S." (And because his S is more of a name than an initial, it can be used on its own without a period, albeit artistically, a period is most frequently used.)
When Truman's parents couldn't come to terms on a middle name, they decided to honor ancestors whose names also began with the letter "S" by giving him the middle name "S." Harry S. Truman is officially written with a period after the letter "S." That's because in his correspondence, Truman paired the letter "S" with a period. The "S" saga is explained in great depth by the Truman Library & Museum. These is the interesting facts about Harry S. Truman.