You are correct on both counts.
I haven't found out if "C" is Clemons. I checked the Miss. & La Confederate Grave register and no "C" Purvis is listed in either. I also did a web search for the 10th Miss. with no luck.
Do you know where he is buried and does he have a marker? There are no clues in his CSR at all, no pension papers, post office etc.?