The way I remember it, the dragoon trainer (or someone in Coerthas at least) explain the dragoons as a contingent of warriors specialised at dealing with dragon-type threats. In each generation there's an Azure Dragoon that's better than the rest because of the Eye. From that, it's safe to say that regular dragoons exist and probably in lesser numbers than the household troops we keep seeing everywhere.
During the Dragoon quests you actually encounter several other dragoons--they were the npcs that would give you tasks to prove yourself worthy (i.e. go kill this, outsider!). There was also a room full of dragoons in one of CSs where we first see the Archbishop of Ishgard. Those dragoons wear the Templer's armor set with bright blue gauntlets. Going by the Heavensward trailer and the set name, the mook dragoons we have met probably belonged to the Temple Knights. The new af might be the uniform of a separate elite Dragoon order not specifically something for the Azure Dragoon. We already have Azure Dragoon AF after all. :)
As far as I am aware the Azure Dragoon is simply just "the chosen one" of all the Dragoons which is simply due to being connected to Nidhogg, now we know that Estinien is still connected to him following on from the final DRG quest as he still hears from him in the 2.55 cutscenes.
You may not hear from Nidhogg as a DRG post 2.55 storyline simply because being linked with Midgardsormr might cause interference or in a similar case grant you greater power than Nidhogg's own, allowing there to be 2 simultaneous Azure Dragoons; Estnien who hears from Nidhogg and Yourself who is connected to Midgardsormr. I am not aware of any point in time where Nidhogg actually speaks to you as the player in the questline so this could easily explain the case.
Alberic: When the being of darkness closed upon us, you appeared to me a spitting image of Haldrath the Dragonseye as he is depicted in the Holy Scriptures.
Alberic: I thought that mayhap the years had taken their toll on my mind, but behold -- the soul of the Dragoon shines as it never did in all the years I bore it.
Alberic: It would seem you have achieved that which was thought impossible; you have awakened to the ability that none but the first Azure Dragoon possessed.
Alberic: I-I can scarce believe mine eyes -- the selfsame armor worn by Haldrath! To think that it had been sealed within the soul crystal all this time...
Alberic: I have borne witness to many and more wonders over the years, yet none compare to you, my young Dragoon. Could it be that you are...?
Alberic: Ahem. Mark not my mutterings. I should rather have said that your indomitable sense of justice resonated with the spirit of the first Azure Dragoon, prompting him to bestow the armor upon you. Yes, that is doubtless what happened.
Alberic: As the being of darkness faded, so too did Nidhogg's aura subside. And now his kind have ceased their stirring. Whether this was compelled by your awakening, I cannot say, I suspect we will learn the truth of it eventually.
Alberic: Estinien, my dear boy... whatever becomes of him, he will ever be as a son to me.
Alberic: I pray that he is somewhere out there still... And that he has not wholly forgotten the great man he once was.
Alberic: When the darkness brushed against me, the selfsame torrent of emotions swept over me as those I experienced fifteen summers past. But there was something else besides. There was a voice that lamented the rift that divides dragons and men.
Alberic: You will comprehend what I speak in due time. Till then <Name>. I pray you will ever use your newfound strength in the name of justice.
The dialogue following the final encounter of the DRG quest does indicate that you are the only Azure dragoon to reach that level of accomplishment since the original which would seem to point out that there are many previous and even current Azure Dragoon's that vary in skill and ability of which you are the greatest since the original Azure Dragoon. Known potential Azure Dragoon's would be the original Haldrath, the zodiac weapon wielder Reinette, Alberic, Estnien and then yourself.