I suspect that was his given name or that of his Masters, as there is only one other man I find in the Confederate army with the surname Carolina and that was Private A. Carolina, 2nd Reserves Virginia Infantry

Carolina
Enlisted as a Blacksmith
"D" Co. GA 1st Battn SharpShooters

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records

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Carolina, Negro/Colored/Black Company Cook, Company D, 1st Battalion Georgia Sharp Shooters,* enlisted by Master August 23, 1862 at Camp Anderson** by Capt. Dent for the war, paid $50 bounty, deserted January 1, 1864 while on leave, it appears he never returned as his name does not appear on subsequent company musters

Note, the regiment at the time he deserted was in winter quarters 3 miles East of Dalton, Ga.

* This company was formed of details from the 29th and 30th Regiments Georgia Infantry and 8th Georgia Battalion and transferred from Savannah Volunteer Guards and 13th Battalion Georgia Volunteers

** Were ordered & took up line of march on 21st Inst. [August, 1862] to a point on Grove River twelve miles from Savannah.

M266: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Georgia

........

Could be:

1860 U.S. Federal Census - Slave Schedules about Carolina L Chambers

Gender: Male
Race: Black
Age: 24
Home in 1860: Savannah City District 1, Chatham, Georgia
Name of Slave Owner: Carolina L Chambers
All Slaves Owned:
Age Gender
21 Female
5 Female
21 Female
1 Female
25 Female
8 Female
24 Male
4 Female
5 Male

The only slaves I find in the Slave schedule for 1860 in Georgia with the surname Carolina are located in Ebert, Ebert County.