It took me a while to find a good name for it, so apologies for anybody used to Holy Anri Nation, but I’m going to translate it as Holy Anri Thearchy instead.
My logic for Holy Anri Nation was basically because the use of the rare (and somewhat made-up) compound, 教国 was more or less limited to uses regarding the Christian or Islamic spheres of influence; something like Christendom or the Islamic State. Because of that, supposing that Anri is more or less their religion, it was appropriate to translate it as the Anri Nation.
Thearchy isn’t really the best word for it, but Theocracy is already taken, and you could argue that Hierocracy is closer to the nuance of 教国, but the term ‘hierocracy’ sort of implies that the power lies with the priests in the nation. Which well, I mean, sort of is true, given how Laissez-Faire Anri is, but basically 神聖アンリ教国 is supposed to demand respect for Anri, so it wasn’t as appropriate in the end.
Hey, this hurts me as well. Holy Anri Nation sounded funnier, and I’ve already named my nationstate after it too. >: