It's pretty obvious what the Volkswagen logo is (a V over a W in a blue background, surrounded by a circle). It's origin is rather mundane though. The logo was the result of an office competition to see if someone could come up with a logo. The winner of the competition (who won 50 Marks for his troubles) was an engineer named Franz Reimspiess (the same man who perfected the engine for the Beetle in the 1930's).
Erwin Komenda, the longstanding Porsche chief designer, developed the car body of the prototype, which was recognizably the Beetle we know today.
The new factory in the new town of KdF-Stadt, now called Wolfsburg, purpose-built for the factory workers, had only produced a handful of cars by the time war started in 1939. Consequently the first volume produced versions of the car were military vehicles, the jeep-like Kubelwagen and the amphibious Schwimmwagen.