German ancestors is a good theory.
The Low German form of that name is Kopper.
Unfortunately, there are no name statistics about German first- and surnames anywhere (DATENSCHUTZ!!!) but when searching
www.telefonbuch.de, I didn't find any Kobber with bb in Germany at all, but some Koppers!
So probably the Kopper surname became Kobber in Denmark.
Hilsen fra
Satu