Nah, correcting them is a good talking point and it doesn't erode their identifiability because they won't accept the correction. CNN, Washington Post, NYT, NPR, etc all say CCP so as far as they're concerned God himself bestowed the name CCP on them and nothing could possibly change their minds. But it can still catch unsuspecting default-libs who look into it and go "hang on, why does every single Western source literally just use an incorrect name for a foreign political party?"