SPOILERS AHEAD:
It seems like Koga is interested in Miya even wayyy before he was possesed by Chiro. I love it. I love a pathetic man. I have a theory that the reason why Chiro is fixated to Miya in the first place is because Chiro is influenced by the Koga's deep-seated interest in Miya. Perhaps that's why Chiro knows Miya's name despite her not even saying it.
Yoru no Shita de Machiawase