In Broadfoot's AOR SUPP, 85, pp. 560-561, there is a roster of the officers of the three (3) companies of Broke Arm's 1st Osage Btln. Captain Black Dog and his more famous father are on the net. The missing Captain of Co. C on the roster is named Wah-ti-in-joh (on his CSR), or Wah-dah-ne-gah (on Don Wise's website).
Washington's Squadron was made up of his Co. A, of Caddo and Arapahoe, and Co. B, of Comanche, commanded by Asapah (on his CSR), or Esopah (Esc Habbe)(according to Thomas F. Anderson, Watie's A.A.A.G., who organized the two companies. It was also known as the "Reserve Squadron". It served in Tandy Walker's 2nd Brigade, Indian Territory Division. Officer are in ibid., p. 580.