Northern Ireland has unionist-associated and nationalist-associated names [1] - using one of them without knowing you're doing so might make people think you've got strong opinions on something you actually don't know much about.
So if you hear someone using a country name you've never heard before, I can understand being cautious about adopting it :)
I don't particularly care about what's official so much as what people use in conversation, but seeing the name of a country change within my own lifetime is an unusual and interesting experience.
Then you may probably be interested in knowing it's just a change in the official code (and I believe quite a number of such changes took place all over the world during your lifetime) and that it even isn't a change but an addition - the "old" name remains ("Czechia" to "The Czech Republic" is what "Mexico" is to "The United Mexican States" or what "Russia" is to "The Russian Federation"). Every Czech or other eastern-European would perfectly understand you if you'd have been using the word "Czechia" in in the past although it wasn't used much in English speech actually. I had even been using it in some semi-official texts in 2008, it wasn't invented in 2013 and wasn't any kind of unacceptable or widely-unknown before.
I don't think it's "just" an official change; whether a cause or consequence of the official change, I've encountered Czech people saying "Czechia" in English a lot more often in recent years than earlier. (E.g. the place I bought my bike from redesigned their website and the new one says "Proudly made in Czechia" where the old one said "Made in Czech Republic"). Of course these things are gradual but I do think it's a real change.
