I was hoping someone else would chime in but.... Most 1861 enlistments were for one year, then two years, then 'for the war', so units went through multiple reorganizations and/or were merged with other units.

The units that essentially remained the same for the duration of the war include:

1st Cherokee Mtd Volunteers aka Watie's Regiment -- Watie/Parks/Bell
1st Creek Mtd Rifles -- D.N McIntosh
1st Osage Battalion -- Broke Arm

These units began service early in the war and then were expanded or combined with other units:

1st Cherokee Battalion -- Joel Mayes Bryan, combined with excess companies of Watie's Regiment to form the 2nd Cherokee Mtd Vols - Adair, in Feb 1863
1st Choctaw Battalion - Battice, expanded to 1st Choctaw Mtd Rifles - Sampson Folsom, in about May 1862
1st Choctaw Cavalry Battalion - Simpson Folsom, expanded to 2nd Choctaw Cavalry Regiment - Simpson Folsom, sometime before 1/1/1863
1st Chickasaw Cavalry Battalion -- Harris/Reynolds/Shecoe, expanded to 1st Chickasaw Regiment -- RW Lee, about 1/1/1865
1st Creek Cavalry Battalion - Chilly McIntosh, expanded to 2nd Creek Mtd Vols -- Chilly McIntosh, about Jan. 1862
1st Seminole Battalion Mtd Vols -- Jumper, expanded to 1st Seminole Mtd Rifles - Jumper, (didn't note the date)

Other units that were in service for part of the war or were reduced:

1st Cherokee Mtd Rifles -- Drew's, was organized in Oct 1861 but defected after Battle of Locust Grove and joined the 2nd and 3rd Indian Home Guard (Union) - July 1862
1st Choctaw & Chickasaw Mtd Rifles -- Cooper/Walker reduced to battalion probably at time of second reorganization in mid-1864
Cherokee Battalion (for Special Service) – Maj Joel Mayes Bryan – after 2/3/63 -- probably a temporary organization
Cherokee Regiment for Special Service in the Indian Territory – Col. J.M. Bryan, May 13, 1865
Deneale’s Choctaw Warriors – Lt Col George E. Deneale, began recruiting in Dec 14, 1861, reached battalion strength about March 1862 but then disbanded (no active service)
1st Squadron Cherokee Mounted Volunteers – Capt. Charles H. Holt, Dec. 12, 1862
1st Battalion Choctaw Cavalry – Lt Col Jackson McCurtain, 1864? became 3rd Regiment Choctaw Cavalry – Col Jackson McCurtain, 1865?
Frye’s Battalion Cherokee Cavalry – Maj Moses C. Frye, 6/3/63 became Scales’ Battalion Cherokee Cavalry – Maj Joseph Absolom “Joab” Scales, 4/23/64
Washington’s Squadron of Indians – Capt George Washington (Caddo), 1865
Wilkin’s Company Choctaw Infantry – Capt John Wilkins, 7/25/1862
Lee's light battery, Capt. R. W. Lee.
Picken’s Company Chickasaw

Others in Indian Territory:

Scanland's Squadron (Texas) was originally part of the 1st Chickasaw Battalion, later added to Well's Battalion
29th Texas Cavalry – Col Charles DeMorse
30th Texas Cavalry – Gurley’s
Lane’s 1st Texas Cavalry, Partisan Rangers – Walter P. Lane
11th Texas Light Artillery – Capt Sylvanus Howell (guns captured at Battle of Ft Wayne)
1st Battalion Texas Partisan Rangers – Capt John L. Randolph
5th Partisan Rangers, Texas Cavalry – Capt Leonidas M. Martin
Gillett’s Squadron (Texas)– Capt. L.E. Gillett
20th Texas Cavalry (dismounted)– Col. Thomas C. Bass, reduced to battalion Feb. 1864
Welch’s Cavalry Squadron (Texas) – Otis Welch
Clarkson’s Battalion (Arkansas) -Colonel James J. Clarkson, disintegrated at Battle of Locust Grove. Those not captured were added to other units.
Wells’ Battalion Texas Cavalry – LTC Wells
31st Texas Cavalry - Looscan
Thomas Livingston's Missourians served and/or encamped in the Cherokee Nation with Watie's Regiment
William C. Quantrill's command operated in the Indian Territory in conjunction with Watie and Adair or when en route to/from Missouri and Texas

And...
1st Chickasaw Regiment - Hunter, this regiment was authorized and officers appointed but never organized. Hunter was discharged by the CS War Dept. The roster of this unit is apparently a fraud.