You would hear the czech language and read the text (whatever language you chose to use) to understand what was said in czech. If you hear english would assume that everything was in english too.
Imagine we are playing a game in some exotic country, that everything we see are that identifies that country as unique are missing (one could imagine that medieval Europe would look the same everywhere you went), a character is called Dong, if we are hearing it in english you couldn’t care less for any references that one could make to east. But if you hear people “dong” a lot, even though the translation doesn’t have the name of the person you could assume that the name also means another thing. Unless extremely obvious when making the dialogs “Oh, so your name means east, eh?”. Which would never happen in a real scenario, thus breaking immersion.
Oh, and if translate the name, well that would be strange too. Thus, once again, breaking immersion.