Bristol historian Bud Phillips wrote a nice story of King's service in the Bristol, TN, paper. He called him Oliver Cromwell King, not Caswell. His service record at Fold3 lists him as O.C. King with service in the 61st TN Mounted Infantry being enrolled at Zollicoffer 10 November 1862 for 34 years. There is no record at Fold3 of service in the 19th TN. In the book "Old Nineteenth Tennessee regiment, C.S.A. June, 1861-April, l865 (1902)" there is no listing for any King name Oliver or O.C.
As for the difference in names, the name Cromwell is a likely name for a Calvinistic Presbyterian, as the Kings were, to give to a child. However, the preponderance of the evidence goes to the family trees calling him Caswell.
Here is the link to Phillips' article: http://www.tricities.com/news/article_4e5a538e-91c0-55df-8e62-d133dd1c7a48.html