Why did Greeks stop believing in the gods?
Because they believed too much.
The ancient Greeks were polytheistic, which means not only that they believed in many gods, they believed in all the gods. In those times that was true of most cultures. The Romans actually considered Jews and Christians to be atheists. We all know they believe in a god. So why would they be atheists? Because they only believed in that one god, but no others.
The Greeks believed in all the gods, and worshipped many, but while there was what amounts to an officially sanctioned religion, they also had significant religious freedoms. Sure some people could be taken to court for "introducing new gods", but that was usually politically motivated and accompanied by other charges, such as "corrupting youth".
This freedom meant that some Greeks worshiped Zeus and Hera and the other Olympians, some worshipped the Great Mother (an import from what is now the Middle-East), some were members of mystery cults, and a few were philosophers. One of the earliest philosophers was Heraclitus, who believed there can only be one god, and that one god is perfect. Heraclitus criticised Homer for depicting the many anthropomorphic gods. How can divine beings have such earthly faults?! They can't so they must not exist. Greeks of his time listened, shook their heads with polite disapproval, much like the English might in a similar situation, and went about their business.
Thus gods spread over the ancient world, and many gods travelled to strange and distant places. The number of divine beings worshipped by the Greeks grew, like all other aspects of culture grow with exposure to other cultures.
And one day, a Jewish fella came to Athens and started preaching about a new god. There was nothing particularly strange about it, a careful analysis reveals he didn't say anything Athenians didn't hear before in one form of another. Yet for some reason this one man much upset some people with his teachings, so he was brought before the authorities to explain himself. It seemed like this might be yet another instance of "introducing new gods and corrupting youth", but the man was well versed in history, trained in rhetoric of the school of Cynics in Tarsus. And thus he knew well how such things were wont to go in Athens. He argued that he saw a shrine in Athens, dedicated to an "unknown god" and was only trying to tell the people more about this god they already acknowledged. He was acquitted and thus the gate was opened to Christianity in Greece.
Over time the Roman empire made Christianity the official religion, and as Greece was a part of that empire, they all became Christians. It didn't happen overnight, but after some resistance the gods of the Greeks were whittled down to one.
The one true God held out for a fair time, although not more than the many that came before. When the scientific revolution killed god, his stab-wounds ran as deep in Greece as they did throughout the rest of Europe. The echo of his dying wail lasted a long time, and in some corners of the world where the land is well disposed towards maintaining such echoes, his cries ring still.
So why did the Greek stop believing in the gods? For the same reason everyone else did. Erosion.
For the same reason the Egyptians, the Romans, the Celts, and the Norse, stopped believing in their gods. They encountered the unifying monotheistic religion of Christianity. Christianity was different than these polytheistic religions. It was promoted as True, Good, superior to, and totally intolerant of other religions or ways of thinking. Why did it succeed? People in the 3rd and 4th centuries CE couldn't help but notice the advantages of the Pax Romana of the previous two hundred years. They could see the advantages of having one unifying government to keep the peace. Of course it would have to be a benevolent government. So why not work toward a centrally controlled empire that was economically and militarily unified under one religion. Keep in mind that these folks did not have any concept of religion as a separate realm of life. Our modern idea of a divide between religious and secular would make no sense to them.
This noble effort of unity didn't quite work out the way it was intended in Western Europe. But the balkanization that followed was later tempered with the concept of a ‘Holy Roman Empire' - an empire that in Voltaire's words, wasn't holy, wasn't Roman, and wasn't an empire. The Eastern Roman Empire, ruling from Constantinople was more successful. But an even more successful version of this quest for religious and political unity emerged from the deserts of Arabia in the 7th century CE. It was a monotheistic religion that would eventually stretch from Al-Andalus (southern Spain) to Indonesia, encountering its most formidable resistance in India, a land with the world's most deeply rooted and complex religious traditions.
They didn't, they changed their names.
They have a patron Saint for every human activity that they had a patron God. It's not Poseidon, it's Saint Nicholas, it's not Aphrodite it's Magdalena, it's not Athena it's Maria, it's not Pluto it's Satan, it's not Charon it's some fallen angel.
In Greek funerals they STILL put the coin under the tongue of the deceased to pay Charon for the crossing of the Acheron river en route to Hades, or their souls will remain in between worlds.
Hades is where all not exceptional people, good or bad, will go.
For the ancients, Hell was for all!
The Elysian Fields, i.e. Paradise, were for the exeptional, for Heros that ascended to a Semi-God status for their unique service to the Gods and Humanity who now are in the company of the Olympian Gods.
The Olympic Games were for the city-states to demonstrate that each of them were protected by such heroes and to honour the fallen Heroes.
My two oboli.
Due to the persecution of the non-Christians in the late Roman Empire: