I'll suggest this thread as a convenient point of reference. Only a handful of Roman gods came from the Greeks (specifically, Bacchus and Apollo, and a few heroes like Hercules, the Dioscuri, and Aeneas).

A couple of key points in the older thread:

• The correspondences between Greek and Roman gods are primarily about translating between languages, and nothing to do with origins. As I put it in the older thread, Mars is the Latin for Ἄρης in the same way that ambulo is the Latin for βαίνω.

• Beyond that, other contexts where Greek and Roman gods were identified with one another are mostly limited to literature and reworked versions of Greek stories. In terms of actual religious practice, there was no overlap between, say, the Roman cult of Jupiter and the Greek cult of Zeus. The big exception is Dionysus/Bacchus. (Apollo to a lesser extent.)

To that I'll add that things get more complicated south of Latium, in Greek colonies like Naples and in southern Italy/Sicily, because cultsites there were Greek ones which continued to exist after those regions acquired Latin rights. It's probably simplest to think of those as special cases, not snapshots of a pan-Roman religion -- they're local cultsites for local people.