My polytheists with competing moon gods are going to have to contend with (what they think is) a new moon, and thus a new moon god, showing up. What are the most plausible ways for them to react to this? We have historical precedents for a new god replacing a local god or gods (religious conversion), and of going from polytheism to monotheism, but I don't know of any cases of a change like this within the context of an existing polytheistic religion. As far as I'm aware the ancient Greeks and Romans and the Norse didn't have new gods added to their pantheons over time, for example. (If I'm wrong about the lack of precedents, I trust that somebody will straighten me out in an answer. In particular, I know very little about eastern religions, so maybe there's something to be learned there.)
They don't see this as some other religion's god, like happens when a religion seeks to displace local gods with a new religion. They have a pantheon of gods with a history/mythology already, and now it appears that those gods' number has increased.
Their pantheon consists of a sun god, the moon gods (one per moon), and an earth god. (There's no overall boss-god.) They don't have specialized gods for other purposes like war, fertility, lightning, and so on.
Their gods have not communicated with them about this (e.g. through prophecy). This doesn't mean that some people won't think they've received such communication, of course.
They're low-tech; they won't be launching probes or even building powerful telescopes to investigate the matter.
My polytheists aren't necessarily human, but when trying to write accessible stories I find myself making aliens either relatable in human ways or very, very different. I'd like to stick to "relatable in human ways" here -- not human, but my reader should think their behavior broadly makes sense.