Some groups add their ancestral grandfather's name to distinguish themselves apart from the other groups that share the same clan surname. Sometimes they do this to separate themselves from a group that is attached to a negative reputation.
For example, just look at the Vue curse. Every Vue will say they aren't that particular group but how do we know? Without a way to distinguish the different Vue groups some clans just simply choose not to marry into that clan surname.
Of course, if you happen to have one of these elaborate clan names and someone does something really bad, you are forever tied to it. Unless you drop that part and just use the plain surname to blend in.