Much of Brokeback Mountain is set in Riverton, Wyoming, gateway to the Wind River Range and Gannett Peak.
However according to the IMDB, the gay cowboy flick was made in the Canadian Rockies near Calgary, Albert; Fort Macleod in Alberta and La Mesilla, New Mexico.
The USGS Global Names Information System shows no Brokeback Mountain although there is a Brokenback Creek/Narrows/Reservoir about 100 miles northeast of Riverton.
Brokeback would seem like a good name for a mountain but I could not easily find it via Google although there is a Brokenback mountain range in Australia.
Riverton is depicted in the movie as a dreary wide spot in the road with a delapidated one-room post office not a booming college town of 10,000 with an airport with commercial service.