Hi /r/AskHistorians, Czechia often also known as the Czech Republic. At least there is a big similarity. It is a bit controversial topic in the Czech Republic for last few years. I would like to know more about it in depth.
You may find the following thread useful, it covers the origin of 'Bohemia' and 'Czech(ia)' and their relation/distinction.
Czechia, although used in the past as shorthand English version of Czech lands, has just been adopted as the official English name for the Czech Republic. Adding the suffix -ia to a country, or place, etc. has its origins in Latin and can be seen all across the globe. Historically it is the lands of the Ethnic Czech Peoples, so adding an -ia gives the land a feminine ending (very common to have the country be feminine).
In Regards to your second question- Czech lands are divided into three historical regions; Bohemia, Moravia, and Silesia. Although Bohemia (North-Northwest) and Moravia (South-Southeast) make up the vast majority of the country. So I'm not sure what you mean by connection between Czechia and Bohemia. Bohemia is a region of Czech Republic (Czechia) and Czechia is now one of the official names, although Czech Republic is still a recognized and official name of the country. Similar to Slovakia can also be referred to the Slovak Republic (As it is also an official name).
Remember these are only changes to the English name.