I think if you combine Matt's and Sam's posts, you have it pretty much right.
Back east the name appears as Shawano, a variant of Shawnee. The Shawnee are a leading tribe of Algonquian Indians, who formerly lived in what is now South Carolina, Tennessee, Pennsylvania, and Ohio. The Shawnee - whose name meant "southerners" - were also called Shawano, Savannuca, and Savannah.
It’s a good guess that the train is named after Mt. Shavano, which in turn was named after Chief Shavano, a medicine man of the Tabeguache band of Ute Indians, led by Chief Ouray. The mountain's most noted feature is the "Angel of Shavano," a large snowfield that (in May and June) is said to resemble an angel with outstretched wings.