Spelling means much more today than it did at the time of the Civil War. Many soldiers couldn't read or write, or did so poorly, so it didn't do much good to ask them how to spell their name. Company clerks recorded most names based on how they sounded.
In my opinion, the possibility of a veteran of the Jeff Davis Legion having a 2nd Miss. Cav. marker is nill. Veterans remembered their command as the JDL and not the 2nd Miss. Cav. Battn., a designation that wasn't used after 1861. It's much more likely that John Renick/Rinick served in the 2nd Miss. Cavalry and just doesn't have a military service file.
Has anyone checked Mississippi pension applications? There is a Tennessee pension application for A. J. Renick, Co. "I", 2nd Miss. Cav. [Reserves], McNairy County TN.