For the mages, how about something like the Order [of the?] Arcana? (Resisting the urge to make a truly awful pun on mage/major there.) And if the technological faction are Communist-y, they'd probably call themselves some permutation of Socialists, which is something real Communists apparently tend towards.
Scepticism and doubt lead to study and investigation, and investigation is the beginning of wisdom. - Clarence DarrowYou seemed to read my mind there. The Order Arcana was the traditional name I had pinned for the Mage faction but it came off as a bit too ordinary. That and this faction is supposed to have several different knightly-esque Orders within itself, so the names would be somewhat repetitive.
Thing is, Arcana has several meanings in-universe, all of which revolve around magic. Arcana is used to describe the practice of magic, the magic establishment, the formal instruction of magic or just anything relating to magic or magical artifacts generally. While it would work in this context I'd like to muddle things as little as possible. It is because of that that it would also be somewhat of a generic name in-universe. Arcana this, Arcana that.
As for the Tech faction, I don't really want any references to Earth social or political systems, as the setting is a constructed world. I feel those terms have connotations and using those words would lend a certain expectation to them that wouldn't serve. I want this universe to have it's own unique in-depth politics and it's own history.
Also, these are Factions rather than Nations, an important difference. The politics of this constructed world is significantly different from ours- these are Factions in the sense that the Alliance or the Horde from World of Warcraft are Factions- amalgamations of the central authorities of several races that make up one of the two predominant superpowers in this world.
There is little sense of strict national identity in this world. Most of what could be called governments are single, independent walled city-states that exert control only over the lands directly surrounding them and even then their grasp is tenuous. As a result of the recent political upheavals there are bandits roaming about and warlords commanding mercenary armies marching all throughout the land, staking claim to whatever territory they can and pillaging whatever weapons and resources can be found. The Factions are the only forces strong enough militarily to really effectively conquer, pacify and politically unify these shattered lands, and unfortunately they are at sharp ideological odds with one-another.
yeyOK, so there's a "steampunk-esque technological faction that has roughly WW 1 level technology and is quasi-Communist". Let's take that description and try to reduce it into a name.
"steampunk-esque technological faction, roughly WW 1 level technology, quasi-Communist"
"steam tech faction, tank level tech, quasicom"
"steam tank tech faction, quasicom"
"steamank tech faction, quasicom"
"steamank, com"
"steamancom"
"Steamancom" seems like a good name, but it probably needs an "of" and another word to go with it. Maybe an "-ists" would do... Steamancomists! Yeah, that might work.
Open a Spanish dictionary and start flipping around syllables.
Also this
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There's also this
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Namestorming:
- Magicrats, Mystics, Arcane, Dreamites, The Kingdom
- Technocrati, Technoluminati, Steamers, The Federation
- Yeah... I suck at naming stuff too.

I am just goddamn terrible at that. Seriously. I will wrack my brain for hours at a time and come up with nothing.
Thing is, I can go on and on about minute details forever when I'm on a roll but when it comes down to the deceptively simple task of naming shit it just stops dead. Take my current active project for instance.
I've been working on it for a while. Got a setting hammered out, a time period, good feel for technology etc. It's gotten to the point where I have large swaths of the history and other details worked out about the setting, but don't even know the names of the two principle factions! I have to keep constantly referring to them by their respective adjectives. And this is by no means limited to just that project either!
Alright, I think that's where I should start, is with the main factions involved. One is a steampunk-esque technological faction that has roughly WW 1 level technology and is quasi-Communist. The other is the reorganized remnants of an ancient order of Mage-rulers now fallen from power.
yey