The name of the Sawatch Range itself derives from a Ute word, saguguachipa, meaning "blue earth." In the Utes' cosmology the mountains and valleys where they lived in Colorado were part of the Blue Earth, or Middle Earth, in contrast to the Lower Earth of deep canyons and the Upper Earth of peak tops. Among their favorite places in Middle Earth was the Upper Arkansas region, where they frequently camped.
The first recorded use of the phrase "Sahwatch Range" came from the report of Capt. John Gunnison's expedition in the 1850s. It was written by Lieutenant E. G. Beckwith, who was actually referring to the mountains on the west side of the San Luis Valley. But the name was later applied instead to the northern chain with its glorious fourteeners.So, from a Ute point of view, either way you spell it, you're spelling it wrong.