Possibly obscure lore question from the Chant of Light

Short answer: The acolyte doesn't have a name because he was not a historic figure. However, it is worth considering the evidence.

The Canticle of Silence is a difficult one. Even before the north and south fell out, the southern Divine had it removed from the Chant in 3:41 as containing too much political propaganda, which is rich considering what a previous Divine did with the Canticle of Shartan. Plus I would say that Drakon's Canticle of Exaltations was similarly convenient political propaganda to justify his self proclaimed stance as the chosen of Andraste tasked with "unifying" the faith. Then only 40 years after it was removed from the Chant the schism occurs between the two Chantries. Now Hessaraian is as much a holy figure in Tevinter lore as Drakon is to the southern Chantry, so removing his Canticle would have been something of a provocation in itself, considering that it must have formed part of Tevinter worship almost from the beginning of their transition to the Maker and thus pre-dated Drakon's version of the Chant of Light by some 150 years.

Now it is likely true that it is political propaganda, considering the heroes of the piece are the acolyte (who rejects his faith) and the Archon who heroically tries to defend his people from the corrupt priesthood of the Old Gods. However, as the preface also admits, Hessarian would have had access to historical records in the Tevinter Archives that might well have detailed at least some of the story that is contained in the Canticle. Obviously the titles of the high priests of the Old Gods would be something of historical record, so that doesn't really prove anything. If the acolyte was a real historical figure, then the details of events up until the point he left the ritual could be the story he recounted to scribes after the event. Then you would have to skip forward to when the acolyte arrives at Minrathous for the rest of the actual historical record, because naturally there were no witnesses left alive of the events after he left the priesthood.

What mitigates against this being anything other than Hessarian's own idea of what happened may actually lie in the fact that no specific names are given. If the acolyte had returned in reality and given this account, surely his/her name would have been recorded. The Archon is just a generic, without being given his actual name. Plus the Archon is said to have confronted the seven High Priests after they fell from heaven, which we know from Corypheus is not true, since he is not even aware if any of the other priests survived. Also the Grey Wardens only discovered Corypheus after the Dumat had been killed and the First Blight ended. Not only that but the Blight began in the Deep Roads and until the arch demon surfaced people were unaware of the danger they faced or any possible connection with their Old Gods. All they knew was that the Old Gods had stopped speaking to their priesthood. It was not until Andraste that a connection was made between the activities of the priesthood of the Old Gods, some 200 years before she was born and the cause of the Blight. As also seems clear from what Corypheus said, they didn't cause it, they only discovered it and there was no confrontation with or booming voice of the Maker, just dead whispers. Which throws into doubt both Andraste's and Hessarian's version of what happened.

So it seems more likely that Hessarian based this Canticle off teachings of Andraste and her disciples that he had heard concerning the origins of the Blight and then expanded them into the Canticle of Silence. So in this instance, the southern Divine may have been right. It was just a piece of inspired political propaganda.

Would just add that if you read the on-line Core Rule Book, it is suggested in there that the Grey Wardens have always had their doubts about the veracity of the account given in the Chant of Light.   Some Wardens even believed that the priesthood had been seeking and found Dumat in the Deep Roads before they went to the Golden City and he assisted them in getting there. Alternatively that there were several groups of the priesthood active at the same time, likely looking for clues as to why their gods had fallen silent, and these various groups were later combined into one for the purposes of narrative in the Chant.    If this is the case, then there could have been some historical records in the Tevinter archives, recording the activities of these groups which Hessarian referenced, including the doubts and objections of some of their acolytes about what they were doing, and these formed the basis of his Canticle of Silence.