Yes, there is a manufacturer's marking on the lid as well as a number (in this case, simply "3").
Regarding their potential usage, I have checked the 1942, 1943 and 1944 editions of the Medical Supply Catalog, and can confirm that Container No. 2 appears to have been a component part of the Chest, Medical Pack, "A", Complete (Item # 97615 / 9761500). Below are copies from the Catalogs showing the entry, along with its contents. I have also included a photograph of the Medical Pack "A" Chest for further reference.
Chest, Medical Pack, "A", Complete (Item # 97615 / 9761500):
I hope that the above information is of some use to you.
Thank you and kind regards,
Ben MajorMRC Administratorben@med-dept.com
1943 Harley-Davidson WLA
1943 Douglas C-47
1944 Cushman 53 Airborne Motor Scooter