It's totally random. It has nothing whatsoever to do with PS. You're making up gods, religions, worlds, demons, definitions for words, and properties of the Azure Sun. It's really not that hard to come up with a decent guild that's not quite so "out there".
Even if everything else was fine, which it's not, wouldn't it be the The Order of Thirteen, or something like that, rather than The Thirteenth Order? You seem to be emphasizing the thirteenth member of your story for some unexplained reason.