Communist Party of China follows the naming conventions used with other communist parties. Examples include: the Communist Party of the Soviet Union, The Communist Party of the United States of America, communist party of Cuba, communist party of Vietnam, The Communist Party of Portugal, etc. That naming convention is simple. You have a communist party located in a country/nation/geographic region/political entity.

Saying “Chinese Communist Party” is meant to place the emphasis on Chinese which in English has ethnic implications. It’s the vision of the party as some kind of Han ethnonationalist movement (instead of a communist movement located in China). Thus, they’re foreigners in Tibet, Mongolia, Xinjiang, and maybe even in Cantonese-speaking China. The history of China as a political entity is handwaved-away.

It’s a subtle difference because “Of China” and “Chinese” can linguistically serve the same function in English. It’s not a purely linguistic difference, it’s mainly the baggage with how the terms have been used.