The Dorian was a 24th century Federation transport. This transport was unarmed, and, in 2369, was under the command of Captain Talmadge.
In that year, the Dorian was on a mission to transport Ambassador Ves Alkar to the planet Rekag-Seronia. En route, the Dorian was flanked by two Rekag battle cruisers who caused damage to the transport's subspace emitter and shields. Dorian was assisted by the USS Enterprise-D, which managed to deter the Rekag ships and would continue the Dorian's mission to Rekag-Seronia. (TNG: "Man of the People")
The model for the Dorian was a reuse of the modified Angosian police shuttle from TNG: "The Hunted".
According to Captains' Logs: The Unauthorized Complete Trek Voyages ( pp. 257-258), this ship was named after The Picture of Dorian Gray, which bore similarities to the episode's story.