Well, it could be a case similar to Col John L. Logan of the 11th Arkansas. After he left the regiment (11 & 17 Consolidated over in Miss and La) he is in command of what is referred to as the 11th Arkansas Cavalry. No such organization existed or was raised....however, many men of the 11th who were captured and paroled after Port Hudson or deserted and returned to Ark joined him under the "11th Arkansas Cav". This is on numerous pensions apps and there is even a partial roster. Logan commanded at times a small brigade and his men referred to themselves as the 11th Ark Cav.
I have even seen men who were from the original 17th Ark Inf, that consolidated with the 11th Inf, who came home and served in Logan's command refered to themselves in the 17th Ark Cav. So Boone could have done the same thing... organized those men of the 15th Inf into a mounted force and they refered to themselves as the 15th Ark Cav as a tie to their old regiment. Of course the 11th was never an official designation and not sure just where the state military assigned them regarding command.