5^th North Carolina Volunteers served as the 15^th North Carolina Infantry Regiment. No one on roll in Company "H" had a last name begining with the letter "U" or a first name begining with the letter "L".

You said the stock was inscribed, "N.C.V. Co.H 5th Regt. CSA". A letter written by S. C. Gay and J. C. Wade on Jan. 23, 1862, Yorktown, Va., is signed, "Co. A 5th Reg. N.C. Volunteers". That's a fairly standard subscription. "N.C. Volunteers" could be abbreviated "N.C. Vols" or "N.C.V.", but that should follow the regimental designation rather than going before the company as you described it.

The letters CSA strike me as somewhat unusual on a contemporary piece. CSA or Confederate States of America appear on official correspondence or items manufactured for use by the army, navy or some other governmental agency. It doesn't often appear in contemporary private communications. I'm no expert on this kind of thing, but unless a soldier expected someone who wasn't a Confederate soldier or citizen to see this firearm, CSA seems like a superfluous designation.