As a big fan of George R.R. Martin's books, I always wondered this. In the Game of Thrones books, the land is made up of seven kingdoms unified by force hundreds of years ago into one state led by a new monarchy. Each kingdom is made up of a couple dozen noble and royal houses, and virtually all characters we meet are members of one of these houses.
They routinely refer to them as entities like this:
Character: "House Stark would never stand by for that to happen. The whole of the North will call their banners and rise to war."
Character: "Their time is over, and House Targaryan is gone. I'll kill every Targaryan I get my hands upon."
Character: "Well, be that as it may, I am a Lannister of House Lannister, and a Lannister always pays his debts."
Martin is a huge student of history, especially the War of the Roses era -- it's an inspiration for his books. Did people in history actually speak in any such way, routinely referring to powerful houses and families in such a formal manner? I sort of assumed it was a fictional cultural thing in the books, but I'm curious.
In ancient Greece, prominent families were usually referred to by the name of their (supposed) original ancestor. For example, the famous Athenian politicians Kleistheneis, Perikles and Alkibiades were all Alkmaionidai, members of the Alkmaionid clan, tracing their ancestry back to the mythological grandson of the hero Nestor from the Iliad. The kings of Sparta belonged to two houses, the Agiad (named for Agis) and the Eurypontid (named for Eurypon) lines; both houses claimed ultimate descent from the Herakleidai, the sons of Herakles.
However, even the members of these families were normally referred to by their name and patronym ("Perikles son of Xanthippos"), not by their clan name ("Perikles of the Alkmaionidai"). I doubt anyone would have used clan names in conversation, or applied them to themselves as an identification. They were more likely to come up in descriptions of political rivalries, since old houses tended to be at the centre of larger factions.
The Alkmaionids specifically were sometimes mentioned in connection with the Kylonian pollution. When the followers of Megakles the Alkmaionid had prevented an attempted coup by Kylon, about 632 BC, they proceeded to stone Kylon's supporters to death while they had sought refuge in a temple. This was regarded as an act of sacrilege that put a curse on the Alkmaionid clan. For centuries after this, there were occasional attempts to banish the Alkmaionids from Athens because of the pollution they carried. Before the Peloponnesian War, the Spartans tried to get rid of Perikles, most prominent politician at Athens, by claiming that it was time for Athens to rid itself of the Alkmaionid curse.