Ok, I see some people are making serious points, so I will reluctantly put my serious face on.
We have precisely one city we can be relatively confident in - Zl is Zlatlan. That's not enough to extrapolate with any amount of confidence, but any guesses - and guesses are the best we can do with so little - should be judged first and foremost by whether or not Zlatlan fits. Beyond that we can pretty much go wild.
Honestly my assumption would be that the modern names mostly are linguistic shifts from the older names that may very well have been much closer to just those two letters.
How much linguistic drift should we be expecting? Itza and Zlatlan are both held by lizardmen, and Quintex is an isolated ruin in Naggaroth. It's likely that there's been less drift, so those names still resemble the originals. But Cl and Cd should then be in the human dominated regions of the Old World and the Far East, which could potentially result in more drift (even accounting for the fact that warhammer languages don't drift much due to being descended from the Old One Tongue).
I'm going to bet against linguistic drift, because these are Old One names. If anything is likely to remain constant through the ages its the names of Old One cities, because those names are presumably in the Old One tongue.
If the polar gates were built by the old ones, would it not make sense that one of the first cities would be built near such an important logistical hub?
I'm not as deep in the names as you are, but there is of course the possibility that whatever Cd was is simply gone now. Buried under the ice and the nurgle mushrooms, or something. Or maybe it's still there, but somewhere inaccessible to anyone who doesn't have extra limbs.
I'm going to tentatively go with "probably not". Partly because the climate in the poles really sucks and I don't think anyone wants to live there, partly because if one of the cities was anywhere near the poles when the polar gates failed I feel like this would come up in Deathfang's tale. We are told the fate of each of the five dragons, and none is "and then they died when a portal to hell opened at their city". But also, Cd is associated with Radixashen who in turn is associated with Athel Loren and Rhya, neither of which is related to anything close to the poles I don't think.
I think we should probably assume they're all on different continents, yeah.
Yeah, I don't disagree that this is probably the case, but:
The problem there becomes what you define as a "continent". Naggaroth, Lustria and the Southlands are covered, but how many continents is the rest of the Old World / Cathay? And should we count the southern continent? Ulthuan almost certainly doesn't count, it was created later on.
This is a big problem imo. It's not even obvious that we should count Naggaroth and Lustria as separate. While we're at it, is Nippon a continent? It's not that much smaller than Ulthuan.
I feel the need to point out that this is Total War, which isn't exactly high on the canonicity scale, but I believe it's the most we got out of Quintex.
Radixashen is also from Total War. If we're gonna do this at all then we must dig into the very depths of the canonity tier. This is the DEEPEST LORE, no source is too obscure.
I assumed it was syllable-based abbreviation, like is sometimes done with Japanese.
This is perfectly sensible. I considered this possibility because it
probably works for Zlatlan, but the issue here is that I am not at all confident in my pronunciation of that name, and also this limits us to two syllable names, which rules out most of my candidate names (though I also toyed with the idea of the first and last syllable, that one probably works even for my list). I agree that Zlatlan is probably Zlat-lan, and your other names work too, so that's a decent guess.
Seems reasonable to think that one is the Lost City of the Old Ones in Khuresh, so we can just treat that one as a 'free space', and it takes care of the Far East (the continent doesn't really have a name the way the others do)
Why not both? The gates of Calith neighbor the hinterlands of Khuresh where the Lost City of the Old Ones is located. We can posit that the gates of Calith were named after the city (either given the same name as the city itself, or using some word derived from it which happens to preserve the Cl syllable strucutre) and narratively it kind of fits that Kalgalanos - whose ultimate fate is "and no one heard of them again" - went off to a poorly fleshed out part of the setting, to a city of which all that is known of it is that it was lost.
Iz being Itza would make sense
The letters probably fit, and I'm tempted to say that "the first city" has to be one of the cities the flight leaders went to, but is that really the case? Sources I found seem to imply that Zlatlan isn't as old as some other cities, it's not obvious to me that it's one of the first five. Still, even if it's not I think that the very first city does seem like the kind of place that a dragon would have wanted to go do.
Iz is where Abraxas went, and the only thing I can find on them is that sigmar wounded them, which probably doesn't fit Itza. But Abraxas also went into exile, so maybe it figures that the city they first went to is far away from where they ended up going later, and also the wiki gives that fact about being wounded by Sigmar without any source so I don't know how seriously we should take it.
I'm still convinced that Morghur's Khazalid name in-quest being Cor-Dum is connected to Cd.
I feel like this makes some amount of sense because Boney went on record as saying that Cor-Dum was given meaning in-quest, and the syllables fit. My main issue there is why would that be the case. Who among the dwarves actually named Morghur Cor-Dum, and did they know about Cd? Why would they?
On the other hand Cor-Dum is the name given to the incarnation of Khsar that hung out around the general area of Athel Loren, which is also where Radixashen went, so a Cd connection isn't out, and as Boney points out:
Khazalid doesn't even have a C, and the only word Mathilde knows with 'kor' is 'Ankor' meaning something like realm, as in the Karaz Ankor (Dwarven Empire) and the Ankor Bryn (Glittering Realm). It might be a linguistic corruption of Gor meaning 'wild beast', but Khazalid generally doesn't get corrupted.
So the Cor really might be from some other language for some reason, maybe from the Old One tongue and that's why it stuck even though Khazalid doesn't get corrupted.
Ok, wild theory time: in Khazalid, Cor became realm Ankor. In Eltharin Cor might have became Tor, which is a city, but also Cor is relatively preserved in the word "Kor", which appears exactly once in all sources in 'Kor Immarmor', which is also a city I think, and Boney guessed Kor means tower or keep or something but it's never defined anywhere afaik. So Cor means city or tower or something like that in the Old One tongue, or maybe it's a very close word to a word in the Old One tongue meaning the same. It's a place, a location. Cor-Dum means is the City-father, corrupted by its betrayal in the tower of Tylos, and so was called Cor-Dum which means "doomed city" or "doomed tower" or something like that, in memory of His origin and His corruption.
This is a very poorly supported idea and it is no help at all with finding Cd, but if I limited myself to well supported theories this would be a much shorter post.