You're right about the name and place part. Böhmen is German for Bohemia and Tschecia (Cechy in Czech) refers to the same region of the Czech Republic, which borders Germany. In fact, the Czech language makes no distinction between the adjectives Bohemian and Czech (Cesky), although I've also read that "Bohemia" related to Poland.
"Historically intertwined" may be the understatement of the year
Borders in this part of Europe seem to have been more a product of rumor than definition.
It seems common for political refugees to be somewhat vague about family names (at least in the public records). After all, there are usually others left behind and matters of ownership and maybe even criminal records to be suppressed. Boehm is more of a location-identifier than a true family name. So is Oberholtzer (the origin of Overholt), which refers to an area around Zurich where that family came from. Of course a name like Oberholtzer would have been pretty useless among the people actually living there -- it only made sense among those who migrated. So the Palatinate refugees called themselves Oberholtzers or Böhmen-ers in much the way that you might choose Thomas Dansk or we might call a Scotsman Robert Highlander (which is pretty much what "Oberholtzer" means).
So I think I also agree with you about the origin of the Beam (Boehm, Böhm) family. My point (and my current fascination) is that they, and an astonishing number of other pioneers of red whiskey making) all ended up farming and making spirits in a particular area of Germany and that became their "place of origin" in the immigration and ship's passenger records. Then many of them migrated again to Pennsylvania, and branched out from there, taking their distilling knowledge with them. And thank you for adding about how the same European war that opened the Palatine area to them also left them with no grapes to make brandy with. Let's see, now, suppose you were already used to making red brandy by charring the barrels, but now you were filling those barrels with distilled rye...
Things that make you go, "Hmmmmmm"? CAN I GET A WITNESS??