Thanks for the responses, but you all misunderstood.
I am not referring to units inside an Army, but to the labeling of an Army by the game when it is first created, when it is still empty.
So, to repeat, when a leader creates an Army inside a city that
does not have a barracks, the Army is labeled as being
"Regular". That label never changes, regardless of the proficiencies of the units subsequently loaded into the Army. To further illustrate my point, here are three pictures of three Armies (all from the same game, but that is irrelevant).
This first picture is a picture of an Army of 3 elite Samurais that was originally created from a leader inside a city that
did not have a barracks:
Notice that underneath my customized name of the Army, it says "Regular". The units inside the Army are actually all elite, but this does not change the original labeling of the Army as "Regular", since it was created using a leader inside a city that
did not have a barracks.
This second screenshot shows an Army of 4 elite Cavalry.
Notice that underneath my customized name of the Army, it says "Veteran". Unlike the Samurai Army above, this Army was originally created by a leader inside a city that
did have a barracks. As with the Samurai Army above, this original "Veteran" label does not change, regardless of the proficiency of units subsequently loaded into the Army.
Finally, here is a picture of an empty Army created at the Military Academy.
Notice that this Army has no label at all underneath my customized name, nor will the game add a label if I load units into the Army.
Again, I am not referring to the units inside an Army, as their proficiencies (Conscript, Regular,Veteran, Elite) do not make a difference in the way the game originally labels an Army (or doesn't label it in the case of the Military Academy).
And before anyone says that perhaps the number of units inside an Army determine its labeling by the game, that is also not the case. Neither the number nor the proficiencies of units inside an Army will affect its original label, only whether or not the originating city had a barracks. The label will say "Regular" if the Army was created from a leader inside a city without a barracks, "Veteran" if the city had a barracks, or no label at all if created at the Military Academy.
I suspect that these labels have no effect at all on gameplay and that they are merely an inconsequential artifact/oversight by Firaxis, but I was just wondering whether anyone can shed any more light on this.