The designation assigned by the War Department was the 3rd Battalion Alabama Reserves. The 3rd Regiment was a different organization. The battalion was also called Strickland's, as it was commanded by Solomon T. Strickland. From my notes:

Company “A” of Tallapoosa, Russell and Chambers Counties “Ready Reserves”

Solomon T. Strickland. Promoted Major. Paroled at Montgomery, Alabama, May 18, 1865.

Members organized at Camp Watts, Notasulga, Alabama, May 30, 1864.