Ennis Del Mar and Jack Twist meet when they work at a Wyoming promontory called Brokeback Mountain. It is the name of the ranch.
None of them do. If you mean Cheyenne Wyoming, you might be thinking of the pepper cayenne which is spelled differently.
Wyoming is the name of a place and does not have a 'middle name'.
The US state of Wyoming was formed from the Wyoming Territory. The Wyoming Territory was part of many different territories over the years, so Wyoming's original name was "Wyoming".
The name of the desert in Wyoming is the Red Desert.
The name of the state capitol building in Cheyenne, Wyoming is "Wyoming State Capitol" or "Wyoming State Capitol Building".
Entrance gate
Barbara Pepper's birth name is Marion Pepper.
There is no community in Wyoming with the name Plymouth.
blood ranch
Silver Moon Ranch
The beauty ranch