What does Drake mean?
English surname-turned-given-name from the Old Norse byname Draki or Old English Draca, both 'dragon', ultimately via Latin draco from Greek drakon 'dragon, serpent'. Flag: it coincides with the unrelated English word 'drake' meaning 'male duck', and the medieval byname's sense is sometimes read as 'dragon/standard-bearer (banner)', so the dragon reading is well-supported but not the only one.
What does King mean?
The English vocabulary word 'king' (Old English 'cyning') used directly as a given name. A transferred surname/word-name rather than an etymological 'king' name from another root.