There are a couple of ways I find the word “polyvalence”* useful in talking about polytheistic religions and beliefs. Some folks use the word “ambiguity,” also a good and useful term.
The first is pretty straightforward, and refers back to my reluctant use of the term “god of” when talking about gods and their areas of interest. Greek gods have many connections. Athena is probably the best known example of this–she is goddess of wisdom, goddess of war, goddess of artisans. That isn’t three Athenas, that is one Athena with a wide range of interests. Other gods may be known for fewer of their multiple attributes but they absolutely do have them.
Epithets are one way of dealing with this sort of ambiguity; in some respects they can act as titles. (Say you lived in a very small town where the town doctor was also the local justice of the peace–you’d call him “Doctor” when he was treating your flu, and “Your Honor” when he was performing your marriage ceremony.)
The other has to do with being multifaith, honoring different pantheons of gods with different (often culturally-related) practices. How can Zeus and Thor both be the god of thunder? How can Hephaistos and Goibniu both be the god of smiths? The significant word there is “the.” If you remove it, there is no problem. So if lightning strikes, do I say “Hail Thor!” or “Hail Zeus!” Well, in my case I’d probably say “Hail Thor!” because my own relationship with Zeus is not particularly lightning-based–other aspects of Zeus are more relevant to my understanding of him. Doesn’t mean that Zeus is not a god of thunder and lightning, just that, for me, lightning is a greater part of my understanding of/relationship with Thor than it is of my understanding of/relationship with Zeus.
* Here “polyvalence” refers to the potential for multiple meanings in a given context.