I have some friends that live in CZ and they still all call it Czech Republic and hate the new Czechia name. This is my first time hearing anyone refer to it by that name before.
I lived here before and after the official name change. Everyone I know still calls it "Czech Republic" - "Czechia" feels weird and unnatural to me.
Additionally it sounds quite close to "Čechy" - what in English we call "Bohemia" - which refers only to the western half of the country (see [1]). So it reminds me a little bit of when people call the UK "England" - so as a Scot living in Moravia I sympathise a little with some locals who feel a bit irked by it :-)
I read recently that one of the leaders of .cz likes the name and one of the leaders hates it.
I'm not a fan because to me it's too similar to Chechnya. In fact, that's what I thought the parent poster was talking about until your comment was posted.