Why would someone make up a middle initial if they didn’t have a real middle name?
Dwight D. Eisenhower. Richard M. Nixon. Gerald R. Ford. John F. Kennedy. Harry S. Truman. No, not Harry S. Truman. Harry just made up the S so he would have something to put between the Harry and the Truman. It also makes his name seem more substantial. Like Edward G. Robinson. Who would have taken a movie star named Eddie Robinson seriously? Eddie Albert, maybe. Or Eddie Murphy. But not Eddie Robinson.
Of course, Harry Truman could have made his name even more serious if he hadn’t used the Harry part either. Harold S. Truman? Harlan S. Truman? Henry S. Truman? What was Harry’s real first name, anyway? And why S? I mean, if you are making up an initial anyway, why not A or X? I would remember an X.
Actually his official name really was Harry S. Truman. His parents named him after his uncle Harry (Harrison) Young. The middle initial was his parent's attempt to please both his grandparents, who both had S in their names. But it didn’t stand for anything. Just S.
“What’s your middle name, Harry?”
“No...your middle name, not your initial.”
Just for the record, the other ones used as examples are “David”, “Milhous”, “Rudolph”, and “Fitzgerald.” (Actually, Ford was born with the name "Leslie Lynch King, Jr." But that's another story.)
Strangely, “Milhous” was also the middle name of George Washington, I think.