I agree-- "the Edge" sounds like the name of an outdoor paintball course that you'd have there. Not a fan.
I'd say go for a two-word name, the second word referring to the landscape, and the first word referring to the history or significance of the location. Like maybe if there used to be an indigenous tribe that lived there, you could name it after them? Like if it was in the Navajo nation, you could have a name like Navajo hills (not sure if the Navajo nation would find that problematic).
Did any of that make sense? The **** if I know. I'm awful at this stuff.