Does the name "Dragon" Age have bigger implications than what we've seen?

Actually with Solas' plans centring around removing the Veil and restoring the world of the elves, he is very much in keeping with the symbolism of the Dragon Age being a time of great change. Before the Veil the dragons ruled the skies. The Evanuris are likely to be released and their favourite alternate form was that of a dragon. They may also have commanded other dragons.

DAI in the end only comprised half the story according to DG. If you look back to the first trailer for DAI in 2013, it shows the Veil being ripped apart, fireballs dropping from the sky (Solas' fiery chaos maybe?) and a big, mean looking dragon seemingly having emerged from the Fade offering a challenge. The sky is uniformly dark and menacing, suggesting the merging of the two realms, just as you saw if you did Hushed Whispers. At the end Morrigan says "will you stand against the dark or lead this world to its bitter end?" Despite all her dread proclamations in DAI, I never got the sense of imminent world apocalypse as seemed to be shown in that trailer, so even if it doesn't occur in the next game, I do wonder if the culmination of the Dragon Age will be Solas dropping the Veil and the hero trying to salvage the situation.

Still, as others have pointed out, Tevinter has a long association with dragons. If they do the scenery correctly according to the lore, then we should be seeing dragon iconography everywhere, on buildings, in pictures, statues. May be we will finally discover the truth about the kossith/qunari relationship with dragons.  Also, as shown in Trespasser, the Qunari aren't above using dragons to produce gaatlok and likely other weapons as well.  I wouldn't be surprised if another dragon cults pops up as well.   So dragon symbolism should abound in the next game.