Given the ongoing but minor arguments about whether the country ought to be referred to as “Czechia” or the “Czech Republic”, I was wondering if the name Bohemia, which unlike the other two has a history of use before the 20th century, was ever considered at the time of the Velvet Divorce. Of course, Slovakia had never been a part of the old Kingdom of Bohemia, so it makes sense that Czechoslovakia did not adopt that name. But once the Czechs and Slovaks separated, was there any suggestion of reviving the Bohemian name?
"Bohemia" is exonym. Its a Latin name for the region that was then accepted as a name for the kingdom in other languages as well. But in Czech language, it was always Čechy, Česko, Češi (with different orthography perhaps Czesi, Czechy). There is no word derived from "Bohemia" in Czech language that would describe Bohemian Kingdom, although one could be easily made.
The "Kronika Wielkopolska" from 13th century is written in Latin and use both Bohemia and Czechy (in slightly different forms). You can read it yourself here.
The "Tusch Chronik von Behem lant" is German 14th century translation of Czech text often called "Dalimilova Kronika" or Dalimil's Chronicle and also uses Bohemia and Czechy, together with the description of the myth about the grandfather Czech. The German text is available here
Finally, there is the Kosmas' "Chronica Boemorum", a Czech chronicle written in latin in the early 12th century that uses only Bohemia (Boemia) and the grandfather Czech is called Boemus. It is, together with a Czech translation, available here.
There are other sources. But what we can learn from those? Its seems that Bohemia and Czech existed alongside each other and were considered synonymous. Bohemia seems to get more popular in the Latin and through it influence other languages, but the term Czech and Czechy wasn't unknown. And as I said previously, I am not aware of existence of Bohemia in Czech language.
Someone more studied might tell you about the relative popularity of Czech and Bohemia in foreign chronicles, but that would be quite a niche topic to study.
So due to Czechia being a name for Czechia in the Czech language for ever, there wasn't any reason to consider Bohemia. At least at that time. There might have been some issues with it in 1918 when Czechoslovakia came to be and a strong German minority might have a problem with being in the state of Czechs and Slovaks. But those are only rumours I have heard and I can't find any source to confirm that.