They didn't. The Roman gods you're thinking of are native, homegrown gods. They eventually became identified with some Greek gods in some contexts, most notably literary poetry.

Many ancient Mediterranean cultures were in the habit of treating foreign gods or even regional deities within their own cultures as alternate names for their own local gods. This enabled them to translate foreign gods into local terminology. You can see this even on a domestic level within the Greek-speaking world: the Laconian 'Dioskouroi', the Samothracian 'Kabeiroi', and the Cretan 'Kouretes' often got equated with one another, for example.

Looking further afield, the Greeks could use either 'Aphrodite' or 'Hera' to refer to the Mesopotamian Ishtar, depending on context, and 'Aphrodite', 'Demeter', or 'Persephone' to refer to the Egyptian Isis. The Romans could use 'Mercury', 'Mars', or 'Jupiter' to refer to the Gaulish Teutates, and 'Apollo' to refer to numerous Gaulish gods of healing.

You'll notice these aren't one-to-one equations: they're one-to-many. But often the divinities were consistent enough that a one-to-one equation could be formed. So for example Greek Adonis = Egyptian Osiris, and Roman Jupiter = Greek Zeus = Egyptian Amun = Phoenician Baal.

A large number of one-to-one equations existed between the Roman and Greek pantheons. That's the basis for the untrue notion that the Roman gods were the Greek gods.

Some Roman religious cults were genuine imports, mind. A number of gods weren't imported from other cultures until the imperial era, like Isis, Cybele, and Christ. Others were earlier, like Bacchus (= Greek Bakchos) and Apollo (= Greek Apollon).

But there are some imported gods who came from the Greeks far back in the mists of the early republican era: in particular, Hercules = Herakles, Castor and Pollux = Kastor and Polydeukes, Aeneas = Aineias, and Ulixes = Odysseus. You'll notice these aren't Olympians: they're all culture heroes, and the last two are a bit more mortal than the first ones. The Romans were primed to be receptive to Greek mythology because the Etruscans had enthusiastically incorporated Greek myths into their own art starting in the 7th century BCE, but what exactly Greek myth looked like in early Rome is not very clear.

For the other gods, like Ceres (Demeter), Jupiter (Zeus), and Minerva (Athena), those aren't imports: they're cases of equating a local god with a foreign god, like we talked about above. It's especially clear in cases where the names are totally different: Zeus and Jupiter do have a shared linguistic root (from *dyēus-(ph₂tēr) 'Dyeus father') -- a shared origin, mind: Jupiter isn't derived from Zeus -- but the linguistic roots of Ceres, Venus, and Mars have nothing to do with the linguistic roots of Demeter, Aphrodite, and Ares.

What happened there is that the equations with Greek gods ended up being popularised. Translating between Greek and Latin meant changing the names: 'Mars' is the Latin word for Ἄρης in the same way that ambulo is the Latin word for βαίνω.

One especially prestigious avenue for popularisation was Roman re-tellings of Greek myths. Ovid's Metamorphoses, for example, tells dozens of stories about Greek mythological characters, but using Roman names, because he was writing in Latin. Those poetic treatments don't mean that Roman religious practice was modelled on Greek practice: the translations don't have any direct implications for that. It's strictly a matter of translating between languages.

I a wrote a longer discussion of this topic a few years ago that has a few more technical details.

Edit: missing word