> Could distros use AnduinDI AnduinUbuntu AnduinLinux. or just Anduin

ANAL, but I'm reasonably sure that the answer is no, they could not, because Ubuntu and Linux have trademark policies that would prevent that.

Also, I disagree; a distro, even a respin, is an operating system, they just don't have a unique kernel which sounds like what you want.

I believe it's fine, as long as you get a sublicense: https://www.linuxfoundation.org/legal/the-linux-mark