Gwen, In looking through my Oklahoma History Books and other resources, I can't find Beginning being named Midland.
The town of Bennington got it's name from Dr. Thomas H. Stark, a descendant of Gen. John Stark.Gen. Stark was in command of the Battle of Bennington in Vermont.
My father, a retired history teacher stated the only other name for Bennington that he knows of was "Tye Town" due to the railroad coming through the area dropping off/storing the railroad tyes in and near the town.
He also had never heard of Midland, but he could be wrong.
Contact the Bryan Historical Society on website-usgenweb and they should be able to help you.
Let me know what you find out. I love a great history story.My hometown is Bokchito, which is 7 miles from Bennington in Bryan Co., so I would love to know. Sherrie