I think what's most important really is the entire logo. Not just a symbol, but the actual word. My favorite is when the symbol is integrated into the text somehow, and then as the icon for the app you "pull out" that.

But again, by just sticking to Halo, you're asking for something cheesy and limiting whatever creativity there is to an extremely small area. Especially with the names not even being Halo-related, it's difficult to have them fit hand-in-hand.

Maybe saying a Halo-related logo can sway a "tie" one way or another would be better. Personally, I think that if we let creativity run wild, we'll get something leaps and bounds better than if we add limitations to it. Those logos I linked to are beautifully designed.