The pistol was originally produced before WWII (1926 by some sources) for sale in Europe. The DUO apparently stands for "Dusek, Opocno" At the time of the German occupation, it was the largest private arms factory in Czechoslovakia (CZ was government owned). The company cooperated with the occupation forces, though Frantisek Dusek himself refused to do so.
Note that I did not say Dusek was the designer; the designer was John Browning, the DUO being almost identical with the FN Model 1906 and the Colt Vest Pocket, so much that some internal parts will interchange.
Well over 100,000 pistols were made up to 1945, most during the war. They were very popular with German officers, who were allowed to buy and carry their own pistols, and most of those in the U.S. were taken from Germans and brought back by American GI's. The DUO was never an issue handgun and was never purchased by the Wehrmacht, so they will not have WaffenAmt markings. The proof marking, a lion over the letter N, is the Czech commercial Nitro (smokeless powder) proof, not a Nazi marking
After the Communist takeover in 1948, the Dusek factory was closed and production was moved to the state-owned Czeska Zbrojovka factory in Uhersky Brod. At that time, the trademark was changed from "DUO" to "Z", and a few were sold in the U.S. before Iron Curtain imports were banned.
One source says that in the 1930's Dusek made the same gun under the names Ideal, Singer, and Jaga. I am inclined to doubt that; both Ideal and Singer were names used by Spanish makers.
Jim