This makes no sense to me. As I have remarked before, it is strange that, almost 25 years after Czechoslovakia ceased to exist people still refer to it as if it is still a country. But I don't think changing the name of the Czech Republic to "Czechia" will stop people from calling it "Czechoslovakia." Changing the name again would just add a third name to the mix, which will certainly not clear up the English-speaking public's confusion about what the country is called.
Plus "Czechia" is just a worse sounding name. Everyone who hears that word is going to confuse it with Chechnya. They would be better off calling it Czechistan. Also I don't think there's anything wrong with the "Czech Republic."