There was this bloke called Duras on Enterprise. The name is old, so is the family and the need to lord over it using a symbol of authority, even if that is just a heriditically passed "name".
I think the leader of the house assumes the name (Romans were big on this as well as adopting adults to create lineage.) of the house, or mothers expecting their children to assume leadership, however unlikely give their kids the name of the leader of the house as the tiniest nudge towards being ambitious, but then it would be kind of pathetic have 1/2 the house having the same "name"? You'd think that the name would be forbidden for any one to use but the ruler of the house?
Popes and Kings take on new names when they get to power.
Remember in King Ralph?
"Maybe you should considering a new name?"
"Why? ralph is a perfectly fine name."