Think I found it : its nickname was Freiburg
That's what I was looking for so you've earned a point.
I'm not sure whether Freiburg was just a nickname or the name given to the car by Autenrieth.
Several of the Autenrieth 502 coupés are known by German city/town names but I can see neither evidence that Autenrieth gave them the names nor that they were just nicknames (given by whom?). Below is a list of most of them (the one highlighted in bold being this puzzle car).
I'll try to find out definitively.
502 F Cabriolet "Bocholt", ca. 15 cars in 1955, 3 survivors
502 Cabriolet "Koblenz", ca. 5 cars, one exists today
501 Cabriolet "Offenbach" 4 Türen, ca. 30 cars around 1954
502 N Coupé "Darmstadt", min. 4 cars in 1956, one exists today
502 Coupé "Hannover", one-off in 1957
502 Coupé "Nürnberg", one-off in 1956
502 Coupé "Marburg", one-off in 1956
502 Cabriolet "Sportwagen Hannover", 4-6 cars 1955-56, 3 survivors
502 Cabriolet "Marburg", 4 cars 1955-56
502 Limousine "Darmstadt", one-off
502 F Coupé "Freiburg", ca. 3 cars 1957-58, one exists today