The Chinese word for Asia is 亞細亞 (yaxiya).
The root of these words seems to be the greek word "Asia", derived from the Akkadian "asu" which means "to rise".
Thus, Asia is the land of the rising sun. But this only has meaning if Asia is seen from the West (historically from the region around the Aegean Sea).
The Chinese historical name of China is 中國 (zhongguo) and means "central region". From the perspective of a Chinese, it is natural to name his own land that way.
But what is the Chinese ancient name of the whole region/continent of Asia?