The word "banshee" is a Gaelic term for a female spirit and the word "reeks" is a Gaelic term for hills and dales. Legend has it that around the 1840s, the owner of the farm was of Irish or Scottish decent. After a night in town he came back to the farm and heard strange cries and sounds in the woods, what he thought might have been banshees.
Since the farm was very hilly, he is supposed to have said that he heard, "banshees in the reeks." In the years since, the name has become Banshee Reeks