The ancient Greek city-states were connected through different customs, although they are often seen as discrete entities. So, even before the city-states started merging with one another, there were common customs and common beliefs.
Since, as you are implying, there was no central authority that "preached" a certain belief, I think you can expect that pantheon of gods would vary in different locations, due to the importance of some gods for whatever reason (e.g. Athena was worshipped greatly in Athens and you can tell that because Parthenon was dedicated to her). There were variations of the Dodecatheon tracing back in older times:
While the number was fixed at twelve, there was considerable variation as to which deities were included. The Dodekatheon of Herodorus of Heraclea included Zeus, Hera, Poseidon, Hermes, Athena, Apollo, Alpheus, Cronus, Rhea and the Charites. The historian Herodotus states that Heracles was included as one of the Twelve by some. At Kos, Heracles and Dionysus are added to the Twelve, and Ares and Hephaestus are not. For Pindar, the Bibliotheca, and Herodorus, Heracles is not one of the Twelve Gods, but the one who established their cult. Lucian (2nd century AD) includes Heracles and Asclepius as members of the Twelve, without explaining which two had to give way for them.
The pantheon (not necessarily the Dodecatheon) could also vary geographically, depending on the regional landscape and included gods such as rivers, who were worshipped greatly due to their importance to the survival and well-being of people living in the nearby regions.
Dodecatheon is a greek word and denotes the set of the twelve main gods.