Harry S. Truman was a 20th century human who served as the 33rd President of the United States from 1945 to 1953.
In 1947, Truman faced several questions following the crash of a Martian spacecraft in Roswell, New Mexico. Known for being an impatient man, Truman demanded immediate answers from base commander General Rex Denning, while limiting the number of individuals participating in the investigation.
Upon the realization that the Martians, later determined to be Ferengi, came from a race far more advanced than humanity, Truman wanted the base personnel to try to talk to with them; a mission assigned to Professor Jeff Carlson.
Once communication was established, and demands were made, the Ferengi leader Quark, threatened to take his business to the Russians if the Americans did not wish to cooperate. General Denning's response was that he did not have the authority to make such a decision, and that he would have to get clearance from Truman.
After relaying the Ferengi demands to Truman, General Denning stated that "that little piano-playing Democrat's not as dumb as he looks." Noting that Truman was not about to make any deals with the Ferengi until they could learn more about them, a task he was willing to leave in Denning's capable hands. (DS9: "Little Green Men")
The Federation starship USS Truman was likely named in honor of Truman. (DS9: "Field of Fire")