I found the following in the Index to Confederate Military Service Records. AL 1st Infantry, Company D.,William W.Hurstprivate H.E.Hurst, private.
An H.E.Hurst also spent time with the AL Talladega County Reserves Infantry, Hurst's Company.Listed in Hurst's Company were George W.Hurst and R.A.Hurst (no William).In Company C of that unit was N.L.R.Hurst. All were enlisted men, privates, so I wonder why the company was attributed to a Hurst.
Dates of service were not given, and I have no idea which service was the initial one.