Re: This is not rebranding
a Slovak here. your post is tad bit, how to say it, economical with facts.
"""Чехия or when using latin alphabet Czechia is how all Slavic nations refer to it anyway and have referred to it even when it used to be Czechoslovakia (to the extreme displeasure of the Slovaks).""""
first, about the displeasure. Czechoslovakia was quite a mouthful, so it was inevitable some shortening would happen. only, having been shortened out of the country does lead to some "displeasure". the feeling was similar to Ukrainians objecting to being called "Russian" (because "they come from ussr, i.e. russia, right?") or Welshmen objecting to being called English, only more so.
now, to that cute russia-centric view of slavic nations of yours (you _are_ Russian, aren't you?)
a short look to https://en.wiktionary.org/wiki/Czechia gives us:
east slavic >>>
belarussian Čechija (or when using cyrillic Чэхія)
south slavic >>>
serb Чешка (or when using latin alphabet Češka)
west slavic >>>
lower sorbian Česka
upper sorbian Čěska
czech Čechy, Česko
slovak Česko (but sometimes also Čechy)
(i left some slavic languages where i was unable to find a translation)
so, you see, not "all". not even "most".
however, there is a grain of truth in what you wrote about "restoration of a historic brand".
even today some people distinguish in Czech between "Čechy" (the Bohemia, or "land of Czech people" proper -- i.e. without Moravia and Silesia) and "Česko" (the whole country), the latter being derived from the adjective in "Země Koruny české" (Lands of the Czech Crown). others use the two terms interchangeably.
hence: Czech is grammatically adjective (for historical reason), the whole storm in a tea cup is about what should its appropriate noun be.
"""At least they are not restoring it to "Moravia" (as that would mean a war with the Slovaks and Southern Polish for the name)."""
I have honestly no idea what could you mean about Southern Polish (or even which Southern Polish).
As far as Slovaks go, we consider Czech to be our brother-nation: we may bicker and tease one another, but in a friendly way (an occasional ice hockey match being a notable exception).
We simply don't wage wars with our brothers over perceived historical grievances.
For God's sake, we're more civilised than that!