CCP has been used for decades by mainly anti-CCP people.
Their official acronym, if ever used, is CPC.
The **ll you say, we always called them Chicoms.
It hasn't been until lately the use of "CCP" show up. I think its a cop-out by some weak-kneed types.
While we're here, and most browsers support unicode, here is what the Chinese 'words' are for communist China:
中国共产党（中共）
Translated it means: Communist Party of China (CPC)