We have 2 variants of device which differ only by battery. Shall we pass FCC separate FCC certification for every of them?
This falls under the topic of "permissive changes".   The FCC has a document called PERMISSIVE CHANGE POLICY which outlines what can or cannot be changed without requiring a new FCC ID.

Under section 2 c). it says, "Part substitution – electrically identical parts may be substituted."

I would assume that the two batteries are the same voltage, but perhaps different capacities (mAh) or chemistries?  For example, allowing for either rechargeable or non-rechargeable batteries in the same package (such as two AA's) shouldn't be a problem.  However if the two battery variants are substantially different in size, it could be argued that would affect the RF performance of the device (since they have a metal casing) and require re-testing.

Your RF testing house may be able to give you some guidance on whether different size batteries would affect the results.