Actually, the answer that would make the most sense to me would be if Lloyd named it Yggdrasill.
Now, why Yggdrasill?
If you're familiar with Norse mythology, which I vaguely was, but didn't figure this out until it was pointed out to me Yggdrasill is the name of the giant, life-giving tree in Norse mythology. Another interesting fact is that the roots of Yggdrasill reach a city called Asgard, and one called Niflheim (which I believe is an optional dungeon in the game. I don't know, being as I had no idea it existed.)
So, it seems there's a few aspects in the game alluding to Norse mythology, which I think is more interesting than Greek mythology. Greek mythology doesn't have an apocolypse story (as far as I know), and I think valkyries are cool too.
Man, I'm such a dork.