@Pyrus: As I said, it varies from ritual to ritual and prayer to prayer. Most of the time I just call on a generic "my Goddess," because I connect to Her best - She's kind of hard to describe, I guess? She's kind of similar to the Christian God in the sense of being an all-encompassing and ultimately loving deity, but also... different somehow. Or maybe not; I don't know - it's been years since I really connected to the Abrahamic God at all.
I may call on different names for specific prayers, however. I've pulled from a variety of pantheons, but because I know the most about Greek, Egyptian, and Norse mythology, those are the ones I draw from most often. I prayed to Bastet to heal my young cat when she sprained her paw a week or so ago (a prayer which was promptly answered), and I frequently pray to and offer libations to Poseidon to prevent seasickness (I get seasick ridiculously easy, but I've found that trading Poseidon milk for nausea prevention works surprisingly well).
@Anna Steen: I... can't say I know a lot about Buddhism, so I can't really comment, haha! I certainly haven't pulled from it intentionally, though I wouldn't be surprised if there were parallels. If anything, I actually got a lot of my spirituality from Wicca, the religion I used to identify with but have since grown away from. There's quite a bit that's changed since I stopped using the Wiccan label, though, so.