our old friend Michael Quinion at World Wide Words provides this A:
A. I am indebted to the American Dialect Society Web archive, and in particular to Jim Rader, for the answer to this question, which otherwise I couldn't find in any of my reference books. The word Dopp is a registered trade mark of a man's toiletry kit. It was designed by Jerome Harris for his uncle Charles Doppelt, a German immigrant to Chicago in the early 1900s. So it's presumably an abbreviated form of Mr Doppelt's family name. The word became widely known during the Second World War when GIs were issued Dopp kits. The company was purchased by Samsonite in the early seventies.
What is even less well known is if a soldier had two of these kits, the one that traveled with him while the other stayed at the base was the Doppelgänger.