Routin Lynn is the farm, the carved rock and waterfall are both called Roughting Linn. They were no doubt one and the same, but over time one has evolved, it's this wonderful evolving thing we call the English language.
The Linn spelling is probably older because Linn comes from the Scottish Gaelic word linne which means pool or waterfall
Maybe the routing or routin part of the name refers to the waterfall gouging out the vale.