But they had very disparate names in their existence
https://en.wikipedia.org/wiki/Skyline_Conference_(1938%E2%80%931962)
Seems most of the schools reference that as the Mount States Conference:
WikipediaThe BYU Cougars are the intercollegiate athletic teams that represent Brigham Young University (BYU), located in Provo, Utah. BYU fields 21 National Collegiate Athletic Association (NCAA) varsity athletic teams. They are a member of the West Coast Conference for most sports. Other sports compete in the Mountain Pacific Sports Federation and as independents. They were a member of the Mountain West Conference from 1999 to 2011 and before the formation of the MWC, the Cougars competed in the Rocky Mountain Athletic Conference, the Mountain States Conference, and the Western Athletic Conference.
https://en.wikipedia.org/wiki/BYU_Cougars#History
WikipediaThe Utah Utes football program is a college football team that competes in the Pac-12 Conference (Pac-12) of the Football Bowl Subdivision (FBS) of NCAA Division I and represents the University of Utah. The Utah college football program began in 1892 and has played home games at the current site of Rice-Eccles Stadium since 1927. They have won twenty-four conference championships in five conferences during their history, and, as of the end of the 2018 season, they have a cumulative record of 677 wins, 464 losses, and 31 ties (.591).The Utes have a record of 17–5 (.773) in bowl games. Among Utah's bowl appearances are two games from the Bowl Championship Series (BCS): the Fiesta Bowl and the Sugar Bowl. In the 2005 Fiesta Bowl, Utah defeated the Pittsburgh Panthers 35–7, and in the 2009 Sugar Bowl, they defeated the Alabama Crimson Tide 31–17. During those seasons, Utah was a member of the Mountain West Conference, whose champion does not receive an automatic invitation to a BCS bowl. The Utes were the first team from a conference without an automatic bid to play in a BCS bowl game—colloquially known as being a BCS Buster—and the first BCS Buster to play in a second...
https://en.wikipedia.org/wiki/Utah_Utes_football#Conference_affiliations
