Penokee is an unincorporated community in Graham County, Kansas, United States, in the Solomon Valley. The community was originally named Reford and platted in 1888 when the railroad was extended to that point. Because the town became mistaken for Rexford, Kansas, the residents renamed their town after the Penokee Mountains near Lakā¦Penokee is an unincorporated community in Graham County, Kansas, United States, in the Solomon Valley. The community was originally named Reford and platted in 1888 when the railroad was extended to that point. Because the town became mistaken for Rexford, Kansas, the residents renamed their town after the Penokee Mountains near Lake Superior.