The government of Taiwan has been willing to maintain the status kayfabe, including maintain the "Republic of China" name and holding China's seat at the UN for a couple of decades. It all seems quite ridiculous from the outside, but a lot of people in the region still get quite pissy about the particulars.

Governments are all 100% kayfabe. They only exist in people's imaginations, same as a game of chess.

CCP just wants power. Expand their sphere and grab the economic flows that would come from that.

So simple.

The official name for the country is 中華民國, or in English, "Republic of China". Its national anthem is called 中華民國國歌. "Taiwan" 臺灣/台灣 is not found in the official name of the country. Sometimes it uses the name "Chinese Taipei" in international organizations.

I’ve heard that action alone triggers an advance from the CCP

More likely it triggers more lipservice but people havent been willing to risk it (nor has there been broad enough consensus in Taiwan to relinquish their own claims to the name and the mainland and the same other territorial expansionist policies that the CCP has, people seem to forget that)