The territory was named after the Wyoming Valley in Pennsylvania, made famous by the 1809 poem Gertrude of Wyoming by Thomas Campbell, based on the Battle of Wyoming in the American War of Independence.
Utterly nothing to do with the game at hand, but I found this interesting:
On December 10, 1869, territorial Governor John Allen Campbell extended the right to vote to women, making Wyoming the first territory and then U.S. state to grant suffrage to women. In addition, Wyoming was also a pioneer in welcoming women into politics. Women first served on juries in Wyoming (Laramie in 1870); Wyoming had the first female court bailiff (Mary Atkinson, Laramie, in 1870); and the first female justice of the peace in the country (Esther Hobart Morris, South Pass City, in 1870). Also, in 1924, Wyoming became the first state to elect a female governor, Nellie Tayloe Ross, who took office in January 1925. (In fact, Wyoming and Texas both elected female governors at the same time, but Wyoming’s took office sixteen days before Texas’s.) Due to its civil-rights history, Wyoming’s state nickname is “The Equality State”, and the official state motto is “Equal Rights”.