Ackchually it’s 中国共产党
The translation could go either way, which is why it was both CCP and CPC before CPC was the officially commented version. The old one has just stuck around since it’s a grammatically equivalent moniker, and nobody really cares. It’s not even disrespectful.
Well, yes, it is the common term used in america. I believe I covered the quirk of transliteration that lead to it’s use. Ergo, american-english affiliated media will likely use the term used in america. Other media will, obviously, use the transliteration common to their culture.