Bruce,
From American Civil War Research database, there are are 6 Beams listed as being in the 1st Chickasaw-Choctaw Cav Regt. aka 1st Choctaw-Chickasaw Mtd. Rifles Regt. Org. July 1861 at Scullyville, with 10 Companies, 6 Companies of Choctaws, 3 Companies of Chickasaws and 1 Company of Half breeds

1. Pvt. Elam Beams Co H
2. Pvt. Elijah Beams Co G
3. Sgt. Isam Beams Co D
4. Sgt. Joel Beams Co I
5. Pvt. Thomas Beams Co F
6. Pvt William Beams Co F

Mike