Equinox would be my guess for the third Lycanroc form.
As in the first day of fall and spring? How would that work, and what does that have to do with day and night? Yes, the term equinox refers to the length of day and night being equal, but what does that mean in the context we're discussing?
Ah, I think I found what you're referring to; I forgot about that, though I'd honestly consider that more a throwaway explanation for the game-specific evolutions than restrictive lore. With that said, the description implies that a combination of Solgaleo/Lunala's influence and time of day are a factor. Theoretically, a third form derived from Necrozma's influence could work just fine with or without time of day being a secondary aspect of it; there's no real reason why it couldn't. It really depends what Solgaleo/Lunala's influence on the whole thing even is, and whether or not Necrozma could have the same sort of influence.
I don't know, those pre-release descriptions normally seem to be up there with Pokédex descriptions when it comes to giving lore to a Pokémon. In the case of some things, like Mega Evolution, it's the only source of lore we have.
To be clear, I don't think it's impossible that a third form based off of Necrozma's influence could exist, I just don't see at as being necessary, and given the awkwardness I pointed about not having anything left to base it off of, I don't think Game Freak will bother. If they do, I won't be surprised, but I will be impressed.
With respect to the counterargument that these games still highlight Solgaleo and Lunala, I very much doubt it. The new forms are almost definitely them and not some sort of weird Sun Necrozma/Moon Necrozma or some construct formed out of Necrozma's armor, I agree, but Necrozma will still almost certainly be the focal point of the whole thing.
Necrozma will be a focal point for sure, and it could easily be "exerting influence," but at the same time, Solgaleo and Lunala will also still be exerting their influences in all likelihood (whatever that even means), which goes back to what I said about not needing to make a new form.
I was just wondering, with the countless rumors of us having news in early august, how likely will we receive USUM news next week? or the week after that?
The rumors have nothing to do with it. Either we will, or we won't. I personally think it's a descent chance that we'll get something over the course of the next two weeks, but that's just based off of logic, not rumors.