Owren is a Norwegian surname.
"The name Owren is the result the name Ofrine (1333), which evolved into Offrenn in 1396, then Ogrem in 1520, then Offrenn in 1578, then Øffrenn in 1594, then Offrem in 1604, then Offrenn in 1668, then Ovren in 1723, and finally, Owren in 1758."
-The Saga of the Owren Family, by Lorayne Owren Leonard.