The first idea is Pantheons - deities can band together into a pantheon for additional help, flexibility, and power sharing. On the other hand, deities can remain aloof, sacrificing those benefits for the ability not to be influenced if their allies are weakened, as well as influence sharing.
The second idea is monikers, which are assigned at the end of Phase 1 of the game (and only then), and, based on how the god was played in Phase 1, will color his or her subsequent time in the game.
Since both things are still very much up in the air, here's a nice little poll... to see whether you'd like one, both, or none of these ideas. P4 rules are still in a state of flux, and I'd like the input of those who will be playing with them

If the Pantheons idea is scrapped, deities will be able to interact with each other more freely (as if none belonged to any pantheon at all). If the Monikers idea is scrapped, there will be no built-in advantages and disadvantages individually chosen for each god.