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Moran (Irish: Ó Móráin) is a modern Irish surname and derived from membership of a medieval dynastic sept. The name means a descendent of Mórán, translated as Big One. Morans were a respected sept of the Uí Fiachrach dynasty in the western counties of Mayo and Sligo. In Ireland, where the name descended from the Gaelic, it is generally pronounced (phonetically) "more-in", an anglicized approximate of the Irish pronunciation. Elsewhere, pronunciation follows the French surname, Morant, anglicized to (phonetically) "more-anne".[ There are many different crests of Moran, all bearing 3 stars and the motto Lucent in tenebris, Latin for "They shine in darkness" ".
The majority bearers of this surname in Co. Mayo are descended from the Ó Móráin sept whose ancient kingdom was in north Mayo, surrounding the modern town of Ballina. Following the Norman invasion their territory was usurped by the Barretts and Burkes and the sept lost its central organisation. The modern distribution of the surname within Mayo suggests that the Morans spread southwards and today are chiefly found in the central area of the county, particularly in the barony of Carra.
There is also a small village in Monaghan named "Moran" meaning abode of "The Great One" the leader of the Celts.

More here :http://en.wikipedia.org/wiki/Moran_(surname)