Game of Thrones the Targaryen Conquest
In the real world, families tend to split apart quickly after a few measly generations. So it makes sense that there are hundreds of noble families.
But in the Targaryen conquests, some nobles have lifespans stretching centuries, and are in the prime of their life for most of that time. Some noble houses have nearly 10 generations living on top of each other.
So the common tradition in westeros, rather than splitting into hundreds of different Houses, they tend to stay as members of the main house. But occasionally, an older couple decides to move out and become a Household.
So a Noble’s name is often their given name, their household name, and then the name of the Highest ranking House they draw relation to.
In the normal system Saris’s name is Saris Shroud. In the Targaryen Conquest her name would be Saris Shroud Baratheon. Often the Household name is dropped for convenience.