I had to call my mother-in-law when I heard about the Star Valley temple, because she lived in that area when she was in the 5th and 6th grades.
She told me quite a few interesting tidbits about the area.
She said Star Valley is a valley, not a town. The main town in that area is Afton, Wyoming, but she lived in a smaller town called Freedom, Wyoming.
Freedom is situated right on the state line between Idaho and Wyoming. The main street of the town has a sign that has "Idaho" written on one side and "Wyoming" on the other.
She said the story she heard when she was young was that in the later years of polygamy (when the members were being persecuted but the church hadn't ended the practice yet) whenever law enforcement officers would come to arrest the men, the polygamists could just walk across the street and be out of their jurisdiction. She said that is why it was named "Freedom".