Designing/Naming the Factions

This is good discussion In my view on WW3, the major world powers like Russia get completely destroyed. Rat, like you said, since everyone is so interconnected, when the government and society falls apart most individuals die. I live NEAR NYC, and can guarantee that NYC would starve in less than a month if they didn't get food shipments. That's basically what I have happen in my story all around the world after/during the war. Most everyone starves because global economic infrastructure falls apart.

In most places around the world, they reach a new population level that can be self-sustaining with local food production and etc. Then in the passing decades they slowly start to rebuild some semblance of society, starting small with towns and villages, like ancient Greek city-states.

Minerva on the other hand wasn't part of the global society. They built a secret bunker, cut themselves off from the world, watched WW3 happen and the world burn, and then waited for their opportunity to emerge with technology and pre-made society when everyone else around them was trying not to starve.

This is a long explanation of the general principles in the world.

To the details of the Mongol faction, whatever there is currently in Russia/Mongolia in terms of technology and organization has probably been lost/destroyed in the past century. They've restarted their civilization from farmers/cattle ranchers/nomads and just now are starting to almost be a nation.