You will learn more from this man's service file, which can be ordered through the message board. You'll see the link at the top of this page.
Also known as the 4th Confederate Regiment, the 34th Tennessee Regiment included three companies from Jackson County, Ala., and a fourth from Hardin County, Tenn., which may have included men from Alabama. Hancock belonged to Capt. T. B. Griffin's Co. "D", which was Company "I" before the regiment reorganized for the war in late April or early May of 1862.
You may also note that Hancock responded to the 1907 veteran's census as a resident of Jackson County, Ala. His name is recorded under the 4th Tennessee Regiment; I'd guess that Hancock told the census taker "4th Tennessee Confederate".