In my SciFi book, 400 years from now, humanity has expanded throughout the solar system and managed to survive the death Earth. In their history, Earth fell during the third world war in 2093 CE and the five existing colonies in the solar system (Luna, Mars, Venus, Callisto, and Titan) were all that was left of humanity. Fast forward 336 years and humanity refers to WWIII as the "Earthfall", the next 49 years as the "Schism" until the five colonies and rogue fleets were united under a single unified government, which is then referred to as the "Formation".

Now with that general background in mind, what would the people of that future refer to our current time period as? (e.g. Middle ages, Renaissance, Industrial Revolution,...etc)

I don't intend for this to be an opinion based question as I am looking for terms that actually might already be used if there are any. Please site a source if it isn't a term that should be easily recognized and I have somehow completely forgotten it. I am discounting terms like "The Digital Age" and "The Modern Age" as everything in the future is likely to continue to be digital, and "modern" means now, which obviously won't be the same for people in the future. Also, if this has already been answered or is too opinion oriented please let me know in the comments.

We already refer to it as the Information Revolution

The use of computers has revolutionised not only the way we collect data and how we use it, but how we think and solve problems. I grew up in a time before Google, and actually learned how to break down a problem into constituent elements, look for keywords, then look them up in encyclopedias. This is a skill that people don't need anymore, like shorthand or even handwriting in some cases.

Our ability to analyse data and derive insights is based on the fact that computers don't need to keep all the moving parts of a puzzle in mind as we do to solve it; they simply follow a set process blindly, allowing us to make key decisions along the way and derive insights from data holdings that it would be impossible to interrogate manually.

Ultimately, information will become the most important asset and resource to many companies (it is already for some) and how we allow those companies to interact with us has already changed massively. The idea of terms and conditions that deal with aspects like privacy, data disclosure and rights in case of a breach were simply unheard of 50 years ago, and given that we now hear job titles like Data Scientist really tell you everything you need to know.

The more interesting question is what the next era is going to look like, and what it will be called by historians.

Very many names could be devised by future historians for the two century period of massive technological advance (and social devolution). No names have come to us from any future time period, so there are no terms that are already being used.

Since there is a devastating war in 2093, the Antebellum Period comes to mind immediately. (Yes, "Antebellum" also refers to the early to mid 1800s in the US, but 400 years from now, no one is even going to know what the US civil war was about or why it was important.)

The great advances in technology might earn this period the moniker the Great Leap or the Second Renaissance.

The general decay of culture might earn this period the name Neo-Medieval Period or the Great Decadence.

I think elemtilas is on the right track with his first suggestion. If the people you are concerned with see WW3 or the Earthfall as the BIG turning point in the history, and they certainly would, they would see the preceding period in terms of the war.

I am not sure why you are talking about Third World War. Maybe it arises from the tensions left by the second world war in the same way the second arised from failure to properly resolve the first world war. Maybe it is just big enough that it must be called a world war and is called the third because there already were two wars called world wars. The difference would matter in the naming.

The time between the first two world wars is often called the Interwar period because it was the time between the two world wars. (duh) So if the third world war is somehow logically connected to the first two ones it could reasonably be called the second interwar period or the long interwar period.

More reasonably the name would be derived from the Earthfall moniker that seems to imply a pretty crucial difference from the first two world wars that would matter to people when thinking about the preceding period.

Pre-fall period would be fairly obvious alternative.

Another alternative would be to look at the preceding period as the wasted last opportunity to avoid what follows and derive the name from that. But I (obviously) do not actually know the causes for the Eartfall and so cannot speculate on that. Period of some sort of foolishness or blindness for sure.

But even the causes for the first world war are still debated. While it is fairly easy to see that political leaders post-Bismarck messed up the system, it is not really simple to name what they did wrong and who the "they" specifically were.

But in general the bad news is that elemtilas is probably right about in which direction the naming happens the unknowable future names this period based on what it considers important which will almost certainly differ from what matters to us. Because of, you know, that huge war that pretty much destroys everything our age built.

The Stupid Ages

This wasn't coined by me, this a brainchild of Matt Groening...

https://theinfosphere.org/Stupid_Ages

The Deforestation Age or The Desertification Age

In hindsight, the key factor might well be what happened to the tropical rainforests, and the follow-up effects of that. Or perhaps other names related to climate change.

The problem with that is that we already had severe climate impact on history and it didn't rate a name.

The Global Age

Trade and investment patterns are integrated to an unprecedented degree. To go with the Age of Exploration, the Age of Mercantilism and the Age of Imperialism, trade patterns might name the age.

The Chinese Hegemony

At least that's what the Chinese would like to see. Other peoples have different ideas, and countries rarely get things entirely their way. Perhaps the Pacific Age.