I'm going to keep my contributions here rather thin since this one's murf's deal and he's totally got this, but to make a few things clear:
Yes, the main moon is named Menphina, regardless of how often they call it Menphina. I do know they've referred to it as the physical manifestation of this deity, but I've never heard them say, "Mm, yes. Full Menphina tonight. Be careful. Menphinatics out there."
Yes, Eorzea seems to be in the Northern Hemisphere. Remember, this game is based on Greece. You can see in the screenshot above that it's right about where Europe would be on the sphere, and the consciousness of the planet has become the mothercrystal seemingly right under these lands.There are some who would have us believe that Menphina and Dalamud are just rocks, the latter in orbit around the former, but such talk is outright sacrilege!
EDIT: Link removed due to screenshot above.