Did the Romans just rename the Greek gods?

No, the Romans did not simply rename the Greek gods, although they did match Roman gods with Greek ones. The Romans identified their own gods with those of the ancient Greeks and reinterpreted myths about Greek deities under the names of their Roman counterparts. But the matching was a translation, not a copy, and it worked in several different ways.

Sometimes the match goes back before either culture: Zeus and Jupiter are thought to derive from a common Indo-European archetype, Dyeus the supreme sky god. Sometimes the match is a stretch. Ares and Mars are both war gods, but Ares was a relatively minor figure in Greek religion and deprecated by the poets, while Mars was a father of the Roman people and central to archaic Roman religion. And some Roman gods had no Greek equivalent at all: Janus and Terminus.

The habit began with the Greeks. Interpretatio graeca is the Greek tendency to identify foreign deities with their own gods. Herodotus, for example, equated Amon with Zeus, Osiris with Dionysus and Ptah with Hephaestus. The scholar Jan Assmann argues that translating the names of gods created the conviction that the gods are international.

Roman religion had a different centre of gravity: because ritual played the central role in Roman religion that myth did for the Greeks, it is sometimes doubted that the Romans had much native mythology. Apollo was adopted directly into Roman culture but developed in a distinctly Roman way, as when Augustus made him a patron deity.