I'm not sure what name you are looking for. That the name Paul Baer relates to the puzzle car engine has already been established, so I can only assume it is not Paul Baer who produced some cars in the period 1921-1924. A Baer engine was also used by Hans Keitel in his designs, but that name has also been mentioned and ruled out.
In 1921 Hans Seehase worked for Joseph Sablatnig, whose factory produced aircraft. I believe that Sablatig was later involved in producing some cars, but I don't know if they had Baer engines, and, in any case, this was after 1921.
Also, some cars (Pawi) were produced in 1921 by Paul Victor Wilkem, but I don't know if he had any relationship to Hans Seehase, nor if his cars utilized Baer engines.