A death certificate won't exist unless someone formally registered the death. As O_G suggests, that might not have happened during the chaos of war. (A funeral director normally isn't meant to bury someone without a full death certificate but, during wartime, it's possible that just an interim certificate from a doctor might have sufficed, with nobody ever getting around to taking that interim document to a register office to formally register the death).
Also, if the person had a middle name, they might have been known to their friends and family by that name, resulting in their middle name being used, instead of their first name, on a death certificate.
If the person's surname sounded German, they might have thought it best to change it when war with Germany broke out.
Those are just a few of the vast number of reasons why a death certificate might seem to be missing.