I can't imagine it being a latinised name of King George III seeing as that isn't really a good name (Georgius or Gorgius.) And I can't imagine it being named after the Prime Minister at the time.
In this POD it is Timothy Pickering who sets this whole thing up, but I can't imagine it being named after him. The main section of the Union is the New England section, then it's Rupert's Land, Lower Canada then Upper Canada (before Louisiana came in.)
Maybe Laurentia but again that's in Canada, one of the less important sections of the Union. But I was also thinking of an aboriginal name but then again that would be Kanata, and then Canada... Or maybe it could be the Penobscot language, suck as their word for home (which I can't find.)
Or I was thinking a simple Nova Brittania.