In any case while Martin openly inspired himself from the British setting in a myriad ways, from the actual map of Westeros and placement of things, to Lancaster vs York etc, the issue here is... I copy/paste again so people see it:
Ok I want to give the King of Brythonia his own vassalized state troops.... while I favor another name than the obvious Round Table Knights - I actually want to call them the Dragon Guard, in honor of the Sarmatian and Dacian dracones standards (remember Britannia was heavily colonized with them in this timeline), I am willing to consider alternatives... Round Table Knights does not sound good to me though, but hey if a lot of people want it...
So what do you want me to name the Brythonia vassalized state unit? You can come up with a new better name of course!