To the "Insiders"

By "insiders", the formal name for China is 中华人民共和国 (People's Republic of China). In short, it is 中国 (literally translated as Middle Kingdom; in short- China). The Chinese generally do not call their country "China" or themselves "Chinese." (中国人 literally means 'middle kingdom person', it is translated as Chinese.) Of course, a Chinese person understands what Chinese and China refer to (if they speak English, many in China do not.)

To the Outsiders

The word China derives from the Persian name for China, Cin which was itself derived from the Sanskrit word pronounced cina (not sure how to get the pronunciation marks). From there, the words cin and cina were likely mispronounced by Europeans who didn't know Sanskrit or the Persian languages. And well... here we are.