In principle an acronym (initialism really) can be an original name, e.g. IBM, BMW. This is common. This trademark seems to have been denied because it's not "original" enough. It's too generic a term.
See also how there's a company named 'Dr. Ing. h.c. F. Porsche AG' with a brand called 'Porsche'. But nowadays that company is just a subsidiary of Volkswagen, and they could restructure to make the Porsche AG disappear, without doing any changes to the brand.
Also, this is literally "people's car".
Had that been the case, and had the phrase been in common use, it would have been impossible to trademark "Bavarian Motor Works" to refer to part of the Bavarian motor works. But reality is different.