In Latin, and in the Harry Potter books, Draco is the word for Dragon. It is also the origin of our English word: dragon (since the most usual form of the word Draco would have an N at the end ... dracon(is), etc). I'll tell you more if you want me to ... most people want to fit me with a silencer at this point!
However, Drake is a surname in English (think Sir FrancisDrake, who sailed around the world for QueenElizabeth the First), so it seems to fit in well as a middle name. Some might still think of some cartoon relatives of Donald Duck, but I don't think it'd ever be an issue. It's pretty unusual for people to even know the difference between a male and a female duck unless they're hunters or poultry farmers.