Double breasted coat, so probably not a private. I assume from your post that your Stephen D Rowe was living in the South? Do you know what State he was living in at the time and what year he was born? Most men enlisted in a regiment that represented the State where they were living so that info would be helpful.
The man in the picture looks too old to be the 19 yo Private Stephen Decatur Rowe, who served in the 6th Virginia. There is another Stephen D Rowe who was a Lieut in the 3d Texas Cavalry; badly wounded and dropped from the rolls; served next as a contracted Asst Surgeon at Winder Hospital in Richmond; and then as an Assistant Surgeon in the 10th Georgia Battalion. He wound up serving in a GA regiment, but he was from Texas. The 10th GA Battn originally served along the coast in GA but was assigned to Wright's Brigade in time for the Battle of the Wilderness May 1864 and remained in that brigade in Anderson's/Mahone's Division of the Army of Northern Virginia until the surrender -- where Asst Surgeon Rowe was among those surrendered at Appomattox. I'm not saying your image is for sure the same man. I'm not a uniform expert by any stretch so, for all I know, it could be a Union soldier in your picture.
Assistant Surgeons had the rank of Captain and even though the title sounds like they assisted the surgeon, they didn't. Some regiments only had an Assistant Surgeon with the rank of Capt but he performed all the same duties as a Surgeon - just without the rank of Major and accompanying pay increase. In fact most Confederate Surgeons originally enlisted as Asst Surg until they could be examined -- even the ones who had been to medical school and been practicing medicine had to pass the exam. If they passed, then they could be promoted to Surgeon and get the rank of Major.