My apologies, but anything concerning myth and/or the Greek language is like a lure to me, irresistable. I'll try to remain innocuous in all regards, however.
Doreen means gift in greek as well
Now, not to say I know this. I don't. I have to look it up. I know that Dora or something near it is gift, as in Pandora, but I'm not sure on the ending. The een is not Greek, that much is sure. Okay... the Lexicon's being kind to me and giving me an easy explanation. It is (dôron) δωρον (oh, apologies for the Greek... this is the first time I have XP, and it allows me to write Greek letters in a forum post. Naturally, I'm ecstatic. Who wouldn't be? Okay, there's sarcasm in that, but it really does excite me.) Anyway, I suppose Dora is the feminine, or maybe Dorê. Doreen probably comes from that, so I'd wager you're right. Just thought I'd support that, out of interests sake.
As far as the term Zealot goes... it is a Greek term, to the best of my knowledge, describing very ardent determination. Okay, I'm turning to the Lexicon again... okay. It's a word used by Sophocles, so that makes it pretty well a native Greek term. Oh, here! This is neat. The Lexicon gives an explanation of how it ties in with Hebrew. It says the Greek term for a Zealot is Zêlôtês (Ζηλωτης), and is the term used to describe the Hebrew Kananitês, which comes from something meaning to glow (Oh, and if you read this Legend of the Past, do correct me if I'm getting anything wrong about this Hebrew, I'm just reading it from the Greek Lexicon.) Anyway, that makes sense, as the Bible, which usually described such things, was written in Greek, and naturally would have made use of a Greek word in translation. So, essentially, it is Greek, and it is the name for the Hebrew freedom fighters. Now, as far as the term for the indwelling of a god goes... it's not zealot, or zealous, but there is one, and I did know it once, earlier this semester. It's the opposite of ecstasy, which I think is 'out of'. I don't think my notes have the term, though.
Anyway, that's that. I just thought I'd comment. I've got a rather great passion for these things, so my eagerness to answer is born out of a rather giddy excitement that they're being discussed rather than anything else.