they should keep the name, b/c the name was in the use, for many years and easy to recognize.
CSA partly changed their name. From Czechoslovak Airlines to Czech Airlines. However, if you follow the there letters, they stand for C(zecho)S(lovak)A(irlines). Now, tell me, where is the "S" in the Czech Airlines. In Czech language, the Czech Airlines means Ceske Aerolinie. Now, one may argue that when speaking Czech, the "S" is in the name. C(e)S(ke)A(erolinie), however it does not make any sense.
Also, the "OK" identification, was established to use in Czechoslovakia. After the split, the Czechs should use "OL" and Slovaks should use "OM". Slovaks use OM, but czechs stick with the OK.
There are two successors after the the split of Czechoslovakia, and they are Czech Rep. and Slovak Rep.. However, the Czech made few tricks, (the airline name, they kept the same flag, etc) so they could be easier recognized around the world.
To the flag. In the history, the old flag was made of three colors. White, Blue and Red. The white and red was the color of Czech lands, Moravia and Slezia (Slesko), the white symbolizes the Slovakia. Now more than 10 years after the split, they still use old flag. Slovaks come up with their new flag.
I could go on and on, but this is not related to the aviation, thus I will stop.
Sorry for any grammar error.