冥靈 mínglíng, a rhyming reduplicative. The name doesn't say what it is the name of. Commentators say it is a kind of tree. There is a tradition among translators of identifying it as a turtle, though for the moment I am at a loss to see where this comes from.
The state of Chu was among the southernmost of the Warring States, so "south of Chu" was virtually beyond the known world. According to the Han Dynasty historian, Sima Qian, Zhuangzi was from the town of Meng in the state of Song, which places him in central China, between modern day Henan and Shandong.