Thanks for that … good question and answers. I was vaguely under the impression Messerschmitt made Bf’s and never stopped to wonder why.
On a broadly similar theme, types like the Magister and Master were for a number of years actually built by Phillips & Powis, although I believe there was a clause stipulating that they would always be known as Miles aircraft and the Miles brothers later bought out P&P and changed the name of the company.