Bill, as usual Danny has more than adequately explained the regimental designation system used by Hindman.

In the case of the 32nd Arkansas, I'm missing one vital date, which is the date on which Colonel Matlock's resignation was approved by the War Department. His letter was dated November 7, 1862, but the resignation wasn't considered official until it was accepted and approved by the Secretary of War. Therefore, the regiment would have continued to be referred to as Matlock's Regiment until Hindman was notified that "the resignation of Colonel Matlock is hereby approved, to take effect from November 7, 1862." It could easily have taken a month for the letter to reach Richmond, and for the approval to reach Arkansas.

Since new elections were held two days after the battle, Hindman had either just received the letter approving Matlock's resignation, or, more likely, anticipated its approval and used the death of Lieutenant-Colonel Young as justification to fill the vacant field officer slots in the 32nd Arkansas.

I hope this convoluted answer makes sense.