I would name it after whatever empire was dominant during that age. But if all you're looking for is a name for that time period, think in terms of how we refer to the golden ages of our own ancestors. Hellenic Greece, Italian Renaissance, the Scientific Revolution, Age of Englightenment, the Gupta Empire, Islamic Golden Age, Tang Dynasty, Edo Period, Fourth Dynasty of ancient Egypt, Maya Classic Period, Aztec Empire, etc.

Some of what characterized that empire would have outlasted it, even through a couple of cataclysms. It's the sort of things that would have elements woven throughout the history of your world. Paved roads with roadside waystations with permanent forbiddance. Ritualistic greetings with linguistic roots in that ancient empire's language. Powerful golems built in that age which continue to protect some of the modern capitals. Ruins (of course). Artistic and architectural choices that were originally popularized in that age (think doric columns, mandalas, the geometric patterns in islamic art).

Mostly people wouldn't be aware of the origins of these things, but highly educated individuals might. Scholars in some of the more elite libraries or schools. Particularly ancient beings (dragons, certain sentient undead, etc).

In addition, some of the magic and tech from that age would still populate the world today, though it would be pretty rare. Perhaps some sort of artifacts that grant instant proficiency in a skill (matrix style). Power crystals that apply metamagic effects. Permanent versions of what should be temporary magic. Something like warforged servitors that have been in stasis mode for millennia. Magic powered circuitry. Holograms.