Now there has been a lively discussion in the community regarding the callsigns in use in this video. For some reason, people can't decide if the unit requesting the fire mission is called "Hot Dog 7", "Hound Dog 7" or "How Dog 7", and I'm interested in clearing this up, but I need help.
I've found information that units were assigned call signs based on the divisional call sign, all starting with the same letter of the divisional moniker (https://9thinfantrydivision.net/9th-infantry-division-history/call-signs/). However, I'm unable to find information for the call signs of other formations to continue looking into which units are involved in the radio call in question.
There has been a statement floating around that the unit in question is "How Dog", but I'm pretty sure that such a unit name would be bad radio procedure, mixing up two very distinct unit monikers. Maybe I'm wrong in that assumption?
Interesting question and like everything dealing with the U.S. Army it has a fairly complicated and sometimes even contradictory answer. The 9th Infantry Division site gives a very good example of how it would work within a division. Basically, the division code governed what all the other codes would be within the division and even with some attached units. For example, the 90th Infantry Division was UNICORN and the attached 537th AAA AW Bn was UNDO.
There were also codes for SHAEF, not so imaginatively, SHAEF, COMZ, also not imaginatively, COMZ, and EAGLE for 12th Army Group. First Army was MASTER, Third Army LUCKY, Seventh Army was CADET, and Ninth Army was CONQUER. Sometimes the terms FORWARD, MAIN, REAR, or SUPPLY were also appended to senior headquarters to identify parts of the headquarters. Now here its important to understand the organizational hierarchy in the US Army. Units were assigned to armies, corps, and divisions as permanent components, but could then be attached to lower echelon units. However, the codes followed the initial letter of their parent and sometimes used the same code word.
Thus, all Engineer Combat Battalions assigned to First Army - MASTER - were MIRACLE, but followed by the battalion number. The 291st Engineer Combat Battalion was MIRACLE 291. Different engineer units, such as Engineer Light Equipment companies were MARGRAVE followed by the company number, and Heavy Ponton battalions were MAYPOLE followed by the battalion number, but Engineer Combat Group Headquarters were given individual M names, such as MAGNITUDE for the 1128th...but then there was the 1142d, which for no apparent reason was AMPERE.
Similarly in First Army all AAA battalions were MAYFAIR, followed by the battalion number, but other AAA units had individual M names, again with the occasional outlier like QUEENLACE, which was Battery C, 226th AAA Searchlight Battalion.
Corps and assigned Corps Troops followed the same pattern, VII Corps was JAYHAWK and VII Corps Artillery was JAMBOREE.
The thing is on D-Day it was all nice and neat, 26 letters in the alphabet worked well for First Army, but as more armies became operational it got more complex, especially when units first assigned to First Army were reassigned to other armies, because units typically retained their original code name, although there was a slight redo on 1 August 1944. Thus, I suspect that QUEENLACE was probably first assigned to the IX Air Defense Command, which was QUESTIONMARK and AMPERE may have been first assigned to ARMOR, which was XIX Corps...or not, its hard to tell now. Similarly, UNDO, the 537th AAA AW Bn, and UNICORN, the 90th Infantry Division, were actually assigned to Third Army and only attached to First Army for the invasion, so the 537th was never given a MAYFAIR designation.
Armored Divisions followed the same pattern as Infantry Divisions where all units followed the same initial letter: 5th AD VOLCANO, 5th AD Trains VALOR, 5th AD CCR VOUCH, 10th Tank Bn VOICE, However, sub-units could be slightly different if they were part of a larger unit. For example, all companies/batteries/troops that were part of a regiment or battalions used the standard phonetic alphabet code following its parent code. Thus, Company C, 10th Tank Battalion would be VOICE-CHARLIE and Battery A, 537th AAA AW Bn would be UNDO-ABLE.
BTW, that meant that no unit larger than a company/battery/troop was given a code name that was in the phonetic alphabet.
Infantry regiments, since they had their own battalions, were slightly different still. All battalions whichever the regiment were RED for the 1st, WHITE for the 2d, and BLUE for the 3d Battalion. Thus, NOSTRIL-RED was the 1st Battalion, 47th Infantry Regiment, but for simplicity Company A was just NOSTRIL-ABLE since everyone knew which company each battalion was. Cannon Company, Antitank Company, and Service Company in the Infantry Regiment were - I know, again not very imaginative - CANNON, AT, and SERVICE (sometimes REAR).
Finally, remember your example is fictional, but we now know it could not be "HOW DOG 7", since HOW was phonetic alphabet for Company H. Nor was there any "7", the officer staff positions were 1 through 6.
Hope that helps.