There is a common misconception of the ancient world as an isolated place, where individual cultures had little intermix besides the occasional and eventual wars. While there is some element of truth to this, there was significant trade throughout the Mediterranean before Rome came to dominate and especially after the conquest of Cathage. The trade of goods and ideas was widespread throughout the ancient world and allowed for cultures to slowly become immersed in the culture of others. By no means was the hellenization if Rome a fast process, it began early in Rome but was sped immensely by the conclusion of the Third Macedonian War until Rome became a massive hellenizing state.

Before Rome came to dominate the Mediterranean, it remained only a local power, fighting amoung at the Italic tribes for supremacy within the central and northern areas of the italic peninsula. The Greeks had created a much stronger cultural and military influence in the south, particularly Syracuse and Tarentum. The Greeks dominated this area until eventually being conquered at the end of the Pyrrhic War in 272 BC. The Greeks, however, had a profound effect upon the Roman world early in its development as it ascended from an Etruscan settlement to the Italic hegemon.

Greek culture was the dominant force in much of the Mediterranean and had dramatic impacts on Roman culture as if developed with Rome acquired mythology from Greece over time, slowly incorporating and comparing Greek mythology and mythological figures into their own. Instead of replacing a Roman god with a Greek god, the stories surrounding the gods were either comparatively similar or made to be similar.

A fundamental idea essential to understanding Roman society and thought was a pervading sense of conservatism, utilitarianism, and adaptation combined with a sense of respect for religions/cultures deemed older and worthy of, at the minimum, respect (this can be seen with Judaism after the incorporation if Judea/Palestine into the Empire). While conservatism and adaptation may seem somewhat mutually exclusive, the gap is bridged by the utilitarianism of Rome, where if something is effective, take it and make it your own. Much of Roman weaponry were developed this way (Gladius, pilum, scutum) as was their culture and religion (art, literature, gods) though still with the sense of conservatism undergirding the developments, vying to remain true to the Roman values/morals of the past.

It would be far more palatable for a Roman citizen to have more stories and material added to your already existing gods than to have a new god replace them. In essence, Romans respected Greek culture and began to include it and the influence grew from Magna Graecia. This is seen later with the adaptation of Christianity to fit Roman holidays and festivals making it far more palatable and lowering the barrier of entry to the new religion. It is far easier to adapt and incorporate than to overwrite a preceding cultural norm to match a new mythological view. The Romans would also absorb gods from conquered peoples which would allow for more seamless integration into the Roman Imperial system, essentially absorbing the people and culture directly into the greater whole of Roman culture and society.

This is particularly evident with Gladiatorial games; cultures/people that had once been enemies of Rome were represented in the arena: the Murmillo represented a Roman legionnaire, the Samnite, the hoplomachus a Greek hoplite, the Thraex as a Thracian, the retarius. Each of these represent a group of people conquered by Rome or come from a culture conquered by Rome. Due to its ability to adapt and absorb, Roman society became a more manageable culture to matriculate into.

Typed on mobile so please excuse any formatting or word choice errors.

I will source when I have access to texts to quote and cite.

It sounds like you're starting from a common misconception, that the Roman gods were all taken from the Greeks. We don't have written sources for the origin of these religions, but there's some good evidence that the religions go back much further and spread all around the Mediterranean. The Etruscans, Romans, and Greeks all had a related religion but they were not taken directly from one another. The stories become mixed later, as the Romans were big into syncretism and mixed just about everything they ran across into their religion.

They're still not identical though. My favorite example is Ares and Mars. They're considered equivalent but their stories are very different, as are their roles in the culture. It's best to just read up on them but one major difference is Mars is literally the father of the Roman people and in many ways the chief deity, while Ares is kind of a dolt and all the "good" aspects of a war god tend to be embodied in Athena instead.