When Avery sent some correspondence to Richmond (I'd have to look and see when it was.) and signed it as Col, commanding 4th Ga. Cav., he received a replay that the records showed him as a Lt. Col. commanding the 23 Btn. and that the commander of the 4th Ga. was Col. Duncan Clinch. Apparently, Gen. Bragg in Middle Tennessee authorized Avery to increace his command from a btn. to regt. and promoted him to full colonel. But apparently, no one bothered to notify the war department in Richmond.
This turns out to be an important foul up, because Avery's attempts to straighten out the confusion over the next 2 years resulted in long pieces of correspondence from him to the war dept. giving the history of his unit. He was, by the way, an excellent writer.
And that is why the unit almost always has his name in parenthesis, to distinguish it from the other 4th Ga.