The Dohlman of Elas was a royal position of great privilege and prerogative, held in high regard by the Elasian people. The proper honorific in addressing her was "Your Glory."
Elaan held the title of Dohlman in 2268. Her arranged marriage to the ruler of Troyius was hoped to foster peace between the two civilizations.
Petri, a Troyian ambassador, referred to the Dohlman as "The thing most feared and hated by my people. Our most deadly enemy." (TOS: "Elaan of Troyius")
Montgomery Scott mentioned the Dohlman when expressing his awe in face of the unexpected luxurious quarters aboard the USS Enterprise-D in 2369, recalling that particular Dohlman, Elaan, complaining about her quarters aboard the original USS Enterprise. (TNG: "Relics")