While in Spain I read that the names origin is the following: In northern Spain near "Covadonga" a few hundred years ago, as the Spanish were starting to force the Moors of North Africa to retreat, the daughter of a Spanish king was made pregnant by a Moore warrior. The name given to the offspring was Moran which in a strange way meant "of the moore".
While travelling in the north of Spain myself, I stopped at a hotel in a small town one night. To my amazement the receptionist told me that my surname was very common in the that town.
I should point out that the north of Spain and especially that town are on the Atlantic ocean. So is Ireland. Travel between the two, although very difficult was possible.
The Irish name Moran (or at least the Irish names from which it has been anglicised) is very old. If the Spanish believe that their name Moran is only a few hundred years old as the story about Covadonga suggests then I would say that the Spanish name probably comes from the Irish name as the Irish one is older.
Please let me know if anybody knows anything about this subject.