Yes, and if the empire were to fall, it wouldn't be ridiculous to assume that they could have banded together on the basis, eh, screw it, we're all still here. Kingdom of Greece!
I think that there's a tendency on these forums, at least in these sorts of debates, from what I've seen, that we all sort of take "Alternate History" as "Things that actually happened, but doing it at a different point."
It'd be an Alternate History thing, but as someone who does do some Alternate History writing, I think that "Kingdom of Greece" is something I could very easily see arising out of the ashes of a shattered empire. I could also see (assuming we're already in the Alternate History where the Byzantines all use the western feudal system for Celestia-Knows-What reason) that someone who's given this king-ish title could say "I don't want to be part of your country anymore" for one reason or another.
Does that make sense?
not really, after the empire fell the Rhōmaiōn people that inhabited modern day greece tried to perserve what had been theres for over 1500 years, they wouldn't just go "Derp well it was a good run, who cares about being the roman empire now, we'll just call ourselves the kingdom of greece!", they definantly wouldn't of chosen the name "greece", you need to realize that greece had been the core of their empire for over 1500 years, they would have no desire to just abandon that, the most likely scenario is that whatever successor state emerged out of the fallen empire, would simply continue to call themselves the roman empire, if there were multiple successor states, then I imagine they would style themselves as despots.