I'm not aware of the particular process by which Hindman revised the name of a unit after the previous commander was replaced.

However, as I'm sure you are aware, Hindman insisted on using the commanders' names rather than numerical designations to identify the various units. From the Alexander Papers, here are some paraphrased extracts that reflect on this issue:

Nov. 21, 1862-General Order # 25 District of Arkansas-
The different Regiments, Battalions, Batteries and unattached companies of this command [other than the Indian troops] will each be designated by the name of the commanding officer of same, specifying also the state from which the men are drawn and the arm of service.

Jan. 4, 1863
Hindman to Chief of Ordnance
...calling his attention to Gen Order# 25, 1862 series, from these headquarters
...on future official papers must use ordered designations for regiments [that is by names of cdrs]

Jan. 4, 1863
Hindman to Marmaduke.... with details as follows regarding a report made by Marmaduke.
1st-the regiments are designated by numbers rather than the names of their commanders, and this is against orders
2nd -the company under Elliott is denominated as a battalion... this is wrong and you are to put that company into McDonald’s command at once
3rd-Quantrill's company is reported by you unattached-this is also against orders and it to is to go into McDonald's command
4th- Seven companies under McDonald are called a regiment by you-this is also wrong-it is a battalion per law and entitled a Lt Col and Major and you will at once organize it as such with the other two companies. You may now get a tenth during the present expedition. If not I will give one of Dorsey’s companies to fill it to a regiment and you can then organize it as such

Jim McGhee and I have discussed exceptions to this situation regarding other units. Hindman's seemingly OCD [as you pointed out] in most cases was contradicted in other instances. A confusing example is Clark's Missouri infantry regiment, which initially had less than the required ten companies but none the less carried the designation as a regiment.