I have asked this some time ago, but have not received a satisfactory answer:

http://www.reddit.com/r/AskHistorians/comments/1jxtdi/how_did_bohemia_turn_into_czechia_in_english/

The basic answer from an English speaking perspective would be fairly easy, as the official shift would be 1918 when "Bohemia" (and other lands) declared independence from Austria-Hungary and founded "Czechoslovakia". However, there are mentions of "Czech" in English from before that. And things get even more confusing when you consider the Germans and Böhmisch/Tschechisch.

But my problem – and a follow-up question to yours – is just when and how did this shift occur? Have the terms been used alongside for a long time? Did the German influence (see above) play a role? And if so, how were those two words used in German? Or is it maybe because of the Boii tribe and the use of Latin in the Middle Ages?

Because from the Czech perspective, nothing changed. The people and the country were still Češi and Čechy or Česko (well -Slovensko, but you get the idea). In the Czech language, there never has been Bohemia OR Czechia, there has been only the one word.