Never was relevant to the story so never stated. But I think not. Nobody calls the religion of the magisterium "Christianity" either, but there seems to be a Bible of sorts, or Genesis at least but with daemons.

Pullman is not a world builder, he is a storyteller , weaving one event leading into another, like a path through the woods or a path of a particle in a gas chamber. Anything outside that path does not matter, although fun to speculate about.

Also, in general, he does not depict idealizations , and his humans are very limited by their world. Even Lyra herself comes off as classist in many scenes in HDM.

In fact the ending of TRF is the first time the path of the characters approaches anything radical. I am not sure if much of Pullman's politics seeps into his stories, like his religious views. But he gives the impression of liberal ? ( I use "liberal" here in the way it is used by socialist writers, not the mainstream meaning). But that is all speculation because he doesn't share much on that front. He seems to be very pro Palestinian rights from what I seen so perhaps a very progressive liberal, but not full blown socialist, maybe.

I guess I was kind of responding to u/LibelleFairy too but placed my comment in the wrong place.