Really, though, we can all accept that DF slowly works at approximating a truly random, brutal, and fantastical version of the Middle Ages, mostly European in nature. Clan names need to passed down directly, otherwise it becomes far too hard for both us and the in-universe @ symbols, e's, H's, and anatomically inaccurate faces with beards to tell who's related to who and why. Eventually, societies should have enough depth to be patri- or matrilineal, since there is almost always some element of that, especially in the Middle Age cultures of Europe. Also, it's a realistic and easy way to track names and clans. Titles should be included. Orphans and low-caste/low-status clan members who gain notoriety should be the ones to found new clans. Also, some method of relating clans (This family is part of the Longbeards clan, founded by Urist McExtremelyflippinglongbeard the Axe-murderer of Beardedness) to each other would be great.
But my point is that somewhere, somehow, there must be a continuum of names. Heck, even if it's a title (Urist McSoggybritches of Longbeardland [as in, a place/structure/small room in somebody else's mansion, which is owned by his long-established family]) for noble dwarves, to differentiate them from common dwarves, who would simply share the last name of their parents.
If that made any sense. Basically, I'm just saying you can't mix-and-match names, otherwise you almost certainly HAVE to have a society that gives no stock to lineage, because otherwise they would, logically, have developed, and developed rapidly, a system of tracking lineage [i.e., OBVIOUS NAMES]