I find it significant (which of course doesn't necessarily mean that it is
) that when Lulu first hears C.C.'s name, he seems shocked (I believe he rocks back away from her). By the time she fully wakes up, he's regained his composure, but I think it's likely that Lulu was quite familiar with whatever name she uttered. Maybe it was the name of a goddess, but ... that seems to me like it shouldn't shock Lulu that much, based on what he's already seen C.C. do.
(So Nina's KF is called Ganymede ... my mind boggles at the possible reasons for this
)