The official site of the University of has many Ute traditions including their alma mater, information about the Crimson Club and the history of their team name:
What is a Ute?
University of Utah athletics teams are known as the "Utes" in honor of the American Indian tribe for which the state of Utah is named. The Utes have inhabited this area of the country for at least 1,000 years. There were originally 12 "Nuche", or "The People", bands throughout Utah and Colorado. The Utes were among the first American Indians to acquire the horse as a means of transportation, and in rock writing the Utes are depicted as horses.
After several armed conflicts with Mormon settlers in 1861, the Utes were relocated to the Uintah Basin in northeastern Utah. Today, tribal headquarters are in Fort Duchesne, Utah, and the Ute Tribe, with a membership of 3,300 and its own tribal government, remains a vibrant part of the state. The University of Utah, in cooperation with the Ute Tribal Business Committee, is proud to share in the tradition of the Ute tribe through the "Utes" nickname.
Source: Traditions (link) webpage on University of Utah Site
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