Zombie threads arise!
Unless things were different back in WWII, government issue (paid for by Uncle Sam) watches had no company logo on the face ... often because they were manufactured by more than one company (and the face had to be "uniform"). Usually, the company's name was etched on the back, along with a serial and/or part number.
Customized watches (commercial watches created for military use) were sold with company names on the front. They were fancier ... and usually sold to proud parents or wives to give to some smart, new graduate of a military school.