No, Wyoming derives from the Munsee (a Native American language) name xwé:wamənk, meaning "at the big river flat", originally applied to the Wyoming Valley in Pennsylvania.
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".
There is no community in Wyoming with the name Plymouth.
The name of Wyoming's state flag is: State Flag of Wyoming.
Cowboy Joe is the name of the Wyoming Cowboys mascot.
The Wyoming Cowboys.
The name Wyoming derives from the Munsee name xwé:wamənk, meaning "at the big river flat."
The name, Wyoming, was used by Representative J. M. Ashley of Ohio who introduced the bill to Congress to provide a temporary government for the territory of Wyoming. The name, Wyoming, was made famous by the 1809 poem Gertrude of Wyoming by Thomas Campbell.It derives from the Munsee name xwé:wamənk, meaning "at the big river flat", originally applied to the Wyoming Valley in Pennsylvania.
"The name Wyoming derives from the Munsee name xwé:wamənk, meaning 'at the big river flat,' but it was also named after the Wyoming Valley in Pennsylvania." [per Wikipedia]
Wyoming was probably the only name considered since the name was used in the bill in the US Congress which created the Wyoming Territory.