"Bohemia" is the foreign name of the land (i.e. Germany vs. Deutschland) while Czech is the name the people who live there have always called themselves. As the nation had been under the domination of German states for many centuries, it was common to refer to the area by the German name, Bohemia (technically, Bohemia refers only to the western parts of the country but it was often used for the whole land similar to "Holland vs. The Netherlands") but once the Czech's became independent they asked the world to refer to them as such, similar to Persia asking the West to call it Iran. It still hasn't been quite settled, as recently the Czech government has begun asking for the English world to refer to it as "Czechia" instead of "The Czech Republic."

As you can see, this question is difficult to talk about without bringing up the very nature of the names of countries themselves and how they are referred to in foreign languages. In general, a nation will have a list of appropriate names that other countries can call it, but this doesn't always work out, such as the Macedonia-Greek naming dispute.