I'm liking the Republic of Anatolia and the Levant - it makes reference to the heartlands.
To be honest I would think the best thing is just for each region to have its own tag: Anatolia or Asia Minor (I'd say Anatolia, though, in line with Turkish
Anadolu; I don't know why a Turkish-dominated state would use 'Asia Minor'), Syria, Iraq... Possibly a formable "Levant"? That's a French word, though. "Mashriq"? Do we have any examples of states that dominated the Mashriq and what they called themselves? This feels a bit like proposing a formable "Maghreb", i.e stupid.
Then if the Ottoman collapse results in an Anatolia-centred polity dominating the Middle East it would just be Anatolia, or if it was dominated by Baghdad it might be called Iraq, or from Damascus Syria. That's a bit odd too, though, isn't it. I particularly dislike "Iraq", it seems like a modern formation. How about
Jazira?
Realistically I would think the most likely outcome of some kind of Ottoman reorganisation into a republican structure would just call itself Turkey (bear in mind modern Turkey controls a swathe of Kurdistan and historical Syria, but still calls itself Turkey). "Turkey" referred to the Turks, yes, but it was also a fairly generic regional term. Such a state would still be centred on Istanbul and possibly Ankara, after all.
I
really like the idea of an option for the Young Turks' "Ottomanism" project to succeed and ultimately produce an "Ottoman Republic".
I don't know what a good name for the proposed (and much fought-for) Turco-Arab dual state would be. Possibly given that it was modelled after Austria-Hungary, Turkey-Arabia? Does anyone know what the Hashemite Arabian kingdom promised in 1916 was going to be called? The various communications I've read in my studies just refer to the "Arab Kingdom", so I guess "Arabia" (that's what the merger of Nejd and Hejaz ultimately got called as well--perhaps "Arabia" in Vic3 can finally be called <dynastyname> Arabia, in line with Saudi?
Is there any place I could read more about these plans? Google gave me nothing.
Another good place to look is Michael Provence, "Ottoman modernity, colonialism, and insurgency in the interwar Arab East",
Int. J. Middle East Stud., 2011, pp. 205-225. He doesn't get deep into the Arabist proposal for a dual state (it's not my immediate area, sorry I can't be more help) but it's a great treatment of how misguided the common narrative of the Arabs being "liberated" from Ottoman rule post-WWI is, and how both Turks and Arabs made efforts to knit the Ottoman realm back together in the '20s and '30s.