When we mention "The Twelve," who do we mean?

 The ancient Hellenes did not have a consensus on the Dodekatheon, or "The Twelve," or even "The Counsel of Twelve." What mattered was that there was a council of twelve, the Dodekatheon, at all. Who resided on the golden thrones atop Snowy Olympos was subject to debate and varied per location.

The most canonical version of the Dodekatheon is represented in a relief currently located at the Walters Art Museum. The relief dates back to the 1st century BC to the 1st century AD and depicts the Twelve Olympians carrying their attributes in procession: from left to right, Hestia (scepter), Hermes (winged cap and staff), Aphrodite (veiled), Ares (helmet and spear), Demeter (scepter and wheat sheaf), Hēphaistos (staff), Hera (scepter), Poseidon (trident), Athena (owl and helmet), Zeus (thunderbolt and staff), Artemis (bow and quiver), and Apollon (cithara). No mention of Dionysos.

There is a story floating about the internet and even some modern texts on Hellenic mythology, that Hestia gave up Her throne to Dionysos. Apparently, this is an ancient myth, and the ancient Hellenes would have believed this as well. It's a story so frequently told, one that is so common-knowledge, that very few people bother to check the source. Well, the source is Robert Graves' 'The Greek Myths', written in 1955. From that book (27.12):

"Finally, having established his worship throughout the world, Dionysus ascended into Heaven, and now sits at the right hand of Zeus as one of the Twelve Great Gods. The self-effacing goddess Hestia resigned her seat at the high table in his favour; glad of any excuse to escape the jealous wranglings of her family, and knowing that she could always count on a quiet welcome in any Greek city which it might please her to visit."

Graves provides two sources for this story: Apollodoros’ Bibliotheka 3.5.3, and and Pausanias’ Hellados Periegesis 2.31.2. As you can read for yourself, there is no mention what so ever of Hestia giving up Her throne. In fact, the sources only address the part of Graves' text that follows afterwards, about Dionysos bringing His mother Semele up to Olympos as well.

So, did Graves lie? Well, yes and no. Graves is a storyteller; he spun stories based on facts he could find. If he could not find a fact, he made it up to fit the story. Because of this, his books are a great read but they are not reliable as far as ancient mythology goes.

Obviously, Theoi who were held in high regard in a certain city-state would have held the thrones, according to the people who lived in that city-state. This means that it's quite likely there were people in ancient Hellas who firmly believed that Dionysos occupied one of the thrones of the Dodekatheon. Most likely, there were also people who believed Hestia did not occupy one of the thrones. It's entirely possible that some people--perhaps even the same people who believed Dionysos was part of the Dodekatheon, but not Hestia--believed that Hestia gave up Her seat to Dionysos. The problem is that there are no ancient sources to support this, and there was most certainly not a wide-spread myth to this effect that held sway in ancient Hellas.

In my personal practice, who hold the thrones of the Dodekatheon is nearly irrelevant. I follow the festival calendar and have my daily ritual practice. through that, all 'major' Theoi are honoured and many of the 'lesser' as well. The pantheon, after all, is much larger than just the children of Kronos and Rhea.