It was about NVidia wanting to make it so their 3rd party GPU partners, (EVGA, Asus etc.), could only sell their popular GPU brands with NVIDIA in them, so for AMD they'd have to come up with something customers are entirely unfamiliar with.
> here's also the issue with them refusing to open source Linux drivers.
It's not just that. AMD didn't open-source their original Linux driver, presumably there could have been some 3rd party licensing issues, but they wrote a new one that is open-source.
NVIDIA doesn't even let others write an open-source driver for them, they make it purposely difficult to reverse-engineer, sign their firmware that they only release with a massive delay and generally refuse to cooperate.