No, that’s just completely wrong. Taiwan’s government was created when Chiang Kai-Shek fled mainland China in the 1950s. It’s the continuation of the Republic of China that governed the entire country of China before the PRC government took over.

Saying that the PRC created the ROC name is ridiculous. The ROC predates the creation of the PRC and is the older name. The PRC didn’t even exist when it was created. Also suggesting that the PRC would ever endorse the ROC in any format is silly. Their entire position is that the ROC doesn’t exist.

You should go read a Wikipedia article on the history of Taiwan as your grasp of the history here is not strong.