Well I wasn't thinking about giving each deity a different religions. After all most people back then were polytheists and thus they didn't mind worshipping several gods at once.
What I was thinking was more that each faction would be able to build temples to various deities. While there are some deities who were more common like Baal and Astarte, there were also some like Milcom and Chemosh who were identified with ethnical groups, or with specific locations or cities like Baalat Gubal or Baal Peor, but all of them were basically gods of the same religion. Most of this is for getting flavor as building temples and restoring temples were a big deal back then and most kings makes a show of how pious and obedient they are towards the gods.
One entirely possible way would be to cut it down to these groups
Polytheism - the normal mood of religion in those days
Yahawism - Hebrew monotheism
Ashurianism - Assyrian monotheism (if you buy the idea that the Assyrians were developing a monotheism with Ashur at the head)
Heresy - various splinters that don't accept the official priesthood and thus are a problem for the rulers