Hi George.
Yes, those numbers are correct. At this mid-war period the average strength of most regiments in the AOT was around 300-400 men.(Before the major actions of Chickamauga, Missionary Ridge etc.). So one company with 34 men equates to a regiment of around 340 (One Company x 10). As the year wore on and military action and sickness wore away the ranks many regiments were amalgamated, this was generally done when regimental numbers fell between 100-200 men. So the 7th Miss. Inf. with (Say 170 in the fall of 1863) would fall within this criteria.
I'm afraid I don't have any further details on names for you.
Regards
Jeff