Kirby, working through the muster cards and prisoner records I find nothing that is contemporaneous with the war labeled 1st NE Regiment until I get to the consolidation of Porter's regiment and "2nd NE MO Cav" Franklin's Regiment. In Col Cyrus Franklin's pay records from the CSA dated 6 April 1863 his regiment is clearly identified as the 2nd Regiment of NE Missouri Cavalry. https://www.fold3.com/image/88540119
He filed for the loss of 2 horses as well one killed at Pierces Mill in action July 13th 1862 and the second at skirmish at Cowskin Mo in McDonald County on Oct 27, 1862. https://geonames.usgs.gov/apex/f?p=GNISPQ:3:::NO::P3_FID:745847
Of interest to the question is Franklin signed these claims as Col P.C.S.A. Does the P stand for Partisan? If so it would lead me to believe Porter's and Franklin's Regiments were part of a Brigade recognized by the CSA under the Partisan Ranger act as the NE MO Cav. at least as of early 1863. Company level designations for 1st NE MO Cav are consistently referred to by Captain's name on prisoner of war records. They almost uniformly refer to Porter's Reg Guerilla's or Porter's band instead of 1st NE Mo Cav. Perhaps because the Union didn't accept the Partisan Ranger Act as valid CSA military units?
A cryptic note about Co A 1st NE MO in the unit organization cards states Co A was mustered Mill Creek, Izzard Co Arkansas Dec 1862 with the note "Some of this company killed before mustered, hence are not included on this roll." So can it be inferred that these companies were not recognized as "official CSA letter companies" until officially mustered by a CSA officer somewhere? There is a note with Co M formerly Hulett's, clearly stating Col Poindexter, CSA mustered the company and it remained in service until disbanded to move south as squads. There is a similar note attached to Co E, known as Capt Wm Dunn's Company. "This company was involved in hard fighting before being organized." These notes make me think that individual's recruited and raised company sized units but they were not "organized and recognized" as official letter companies until officially "mustered" into the regiment. There is a card referring to JW Porter, Capt. Mustering and Inspecting Officer. The Co B card clearly states Company B formerly known as Capt. Chas Powell's company. M/I Ralls County, HG Snider.
Of interest to us is the info on Co L, organization record. It is identified as Co L also known as Young Percell's Company. The affidavit states "I certify that I have examined the men upon this muster roll and their horses and have accepted them into the Confederate States Service for the term of service of twelve months." signed Edward R Freeman Inspecting and Mustering Officer August 3 1862.
I don't know if this answers your question but leads me to believe there was a degree of organization and recognition of what was going on and who was what with the designations of the Regiment and Company Letters not being just a histography tool after the fact. With that said I suspect at the soldier in the field level the knew who their Capt was and they joined a particular recruiter's company and identified with that group much more so than an esoteric designation from Richmond Va.