There are many cafes run by dolls in the version of Miyagi Prefecture that appears in the world of Confluence and its sequels, so it seemed to make sense to write their beings as part of a union.
I picture it as an outgrowth of an older union focused on bakers when originally founded, which means I can make it into a bilingual pun: パン宮城人形組合 Pan Miyagi Ningyō Kumiai -- which is both "Pan-Miyagi Doll Union" but also "Miyagi Bread Doll Union," as "pan" is the Japanese word for "bread."
Ever and always, I can't resist a pun.