Yep - it's the feminine form of the adjective meaning "Czech" ("republika" being "republic" - a feminine word). Not to be confused with the similar "Čechy" which refers to Bohemia - the western half of Czech Republic.

I'm not sure why Czechia wasn't pushed from the start. Might be worth remembering that the official name for Slovakia is actually "Slovak Republic" - so maybe their short version only caught on since people were used to the "-slovakia" part of Czechoslovakia?