Gregory Clark, an economic historian at the University of California - Davis, has a nifty paper on the persistence of surnames in England from the 1200s to now. He was looking for how much specific family names stayed in the same class.
Clark's conclusion is that family names seem to cycle in and out of the top and middle classes (at least) over about six generations. He concludes from this that there are not really permanent classes in Britain, a famously class-ridden society.
Clark offers some important caveats, and the interesting suggestion that it is only now, in the more meritocratic society that was supposed to end family privilege, that there is actually greater persistence of the same families in the same classes. He cannot demonstrate that point in this paper, but I hope he follows up.
On the one hand, it is good news for the happy society that the "regression toward the mean" pushes social mobility. Privilege does not last forever, or even very long. Nor does subordination.
On the other hand, showing that families move in and out of classes is not at all the same as proving that there are no classes. On the contrary, he has to use some persistent features of the class structure, such as the amount of estate tax paid, as his measure of which class a family name is in.
Lineages are mobile, up and down, which is good news. But the class structure endures, which is a basic fact of modern societies.