My knowledge of that area is sorely lacking. But if I remember right it was called Bohemia for the longest time. Why and where did Czechia come from? Is it because Bohemia was their Germanic name and they tried to distance themselves from the days of the Holy Roman Empire?
Until a better answer is provided please see this thread, the same question is answered there.
Bohemia is the name of a region in the western part of the contemporary Czech Republic, but the Czech Republic also includes Moravia and (part of) Silesia. These are part of the historical "Bohemian lands", and they are inhabited mostly by Czechs, but they are not Bohemia. So on the one hand, you can't call the Czech Republic Bohemia because Bohemian and Czech are not the same thing.
On the other hand, in the Czech language, Bohemia and Czech kind of are the same thing. The Czech word for Bohemia is "Čechy", and the adjective "český" and the noun "Čech" (describing a person) can be translated as either "Bohemian" or "Czech", depending on the context. Moravia and Silesia were always somewhat peripheral in the Bohemian kingdom and the Czech national movement, so this makes sense. With the development of Czech nationalism, people started understanding "Čech" and "český" to mean Czech rather than Bohemian when referring to people, language, etc., although it did take a while outside of Bohemia.
So there's no word in Czech like "Bohemia" that the Czechs could have used to name their country in 1993. If you wanted to translate "Bohemian Republic" into Czech, it would be "Česká republika", which is what the Czech Republic is called. Medieval and early modern Bohemians writing in Latin did use the term "Bohemia", but it has never existed in Czech. Some people do call the country "Čechy" informally, but other people hate this, either because they are sticklers for precision or because they are Moravians or Silesians.