Badge engineering goes back a lot further than the examples quoted. Directly related to this forum, both Minerva and Tempus produced badge engineered Landrovers in the fifties, as did a number of other companies such as Santana more recently.
The oldest one I can recollect seeing in the metal (actually only part of it) was a "Peerless" from the early 1020s - which bore a striking resemblance to Henry's products, but there were others as well, some going back to the nineteenth century.
But more recently than these examples, not quite the same badge engineering, but very similar, was where a company 'A' took over or merged with company 'B', and continued to sell both makes 'A' and 'B'. This became very popular from the 1920s on in the shakeout of the industry following WW1, especially in Britain (e.g. Rolls Royce/Bentley and the Rootes Group) and again from the 1950s with BMC, where the same car was produced and sold by the same company with different badges and slightly different metal and trim.

