I've run a few adventures in 4E now, and I am still working on the rules. I've been running in a kind of parallel worlds: the D&D Points of Light generic campaign world, and my long running and non-running Malaan Game. I love Malaan, so I wasn't going to abandon it, but every game rule shift causes a bit of turmoil. Since we were all beginning a new game system, I wanted to leave all the "flavor text" available to the players, and kept the core rules for that.
There is term in the philosphy of religion called "Syncretism." Basically, this means when one culture meets another, they tend to adopt bits of culture and religion here and there. The Greeks taking on the mystery cults of Isis and Dionysus from Egypt and Asia. The Romans taking on the Aryan cult of Mithra. The Mayans adopting a Christian faced to the their pantheon in the forms of the Santos religion. Frequently it involves adopting elements of the one religion but incorporating it into the existing pantheon (Mithras becomes a version of Jupiter, St. Peter is Quetzalcoatl etc.).
So far, I haven't done much. I made it clear that the Core D&D Gods are those recognized by the natives of the lands they live in . However, their worship is somewhat new (100 years or so, very vague), and the world had many other religions before that.
One player recently expressed an interest in playing a Cleric of the Raven Queen (generic death goddess of the Core PHB). Of course, you my good readers know of the extensive dominant death cults of Malaan (the Deh'wheri). Some of you are privy to the more history where the worship of Velrey dominated that cult, and gained control of the holy lands. So... here is the syncretism.
The Raven Queen is named for a mysterious death goddess who sent a Raven to a local woman to counsel her on the anniversary of her husband's death. In my mind, this an attempt by Auteil (former head of the Deh'wheri) to reach out to a new audience under cover as it were.
So everyone can use the core gods, but slowly they will be revelaed to have this much richer, deeper connection with my world.
(I remember when Ben slowly converted from the D&D gods Donblass, Arioch, etc.. to his own with variant names and following). Same thing here.