The Dorian was an unarmed 24th century transport ship. In 2369, it 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")
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.
For more information on this studio model, please see TNG studio models.