Like most everything else in the Confederate government, what started out as a standard procedure early in the war became subject to expedience as the war dragged on. That being understood, the system begins with a request from the Confederate War Department for additional regiments. The State Military Board was responsible for raising, equipping and designating the regiments. Once the regiment was organized, it was inspected by a representative of the regular Confederate Army who, if he found it to be ready in all respects for active service, accepted the regiment into Confederate service for a specific period of time. At this point, the Confederate government was responsible for paying, clothing, and feeding the regiment. Most financially-strapped State governments quickly ceased equipping regiments, relying on the Confederate States to take care of arms. Anyway, the State Military Board kept a roster of regiments raised in the State, and sequentially numbered them, based on when the regiment was authorized (not necessarily when it was mustered into service). The Confederate War Department normally went along with the State numbering scheme, but sometimes interfered, especially in the early part of the war. That's how they ended up with with two 1st Arkansas Regiments, three 19th Arkansas Regiments and three 15th Arkansas Regiments.

During the reorganization of the Trans-Mississippi Army following the battle of Prairie Grove, the commander of the Trans-Mississippi Department got into the numbering game, too, and redesignated a bunch of regiments, e.g., the 28th became the 36th, the 29th became the 37th, etc.

And, of course, the division and brigade commanders had to get in on the act, too. At one point, the 34th through 39th Arkansas regiments were redesignated as "Trans-Mississippi Rifle Regiments". Also, some brigade commanders (especially cavalry brigades) arbitrarily redesignated their component regiments, so that you ended up with a whole passle of 1st and 2nd Arkansas Cavalry regiments.

And finally, regimental commanders (especially in the cavalry) sometimes adopted their own designations. Seems everyone wanted to be known as the "1st Arkansas Cavalry" -- so the 4th, 6th, 10th and 12th Arkansas Cavalry regiments are often referred to as "So-and so's 1st Arkansas Cavalry".

Well, I seem to have strayed quite a bit from your original question -- when was a designation "official"? Theoretically, the official designation was the one assigned by the State Military Board when the regiment was authorized, and confirmed by the Confederate War Department when it was accepted into Confederate service.