As mentioned, patronymic suffixes denote lineage via a parent's name, rather than via surnames. Therefore, your father's name (or sometimes your mother's name) has "son" or "daughter" appended to it, depending on the gender of the person in question. Such things occur in British names, but only in an historical context (e.g. Johnson was originally a patronymic name - lit: John's son).
Iceland is one of the few countries to still use this system. The female suffix should be d?ttir, not merely dottir.
Oddly, you often have cyclic naming in Iceland, with children being named after their grandparents. Perhaps more bizarrely, from a foreigner's point of view, families can have several "surnames", because the mother and father take their parents' names, yet the children take (typically) the father's name. And, of course, if the offspring are of mixed gender, they have different "surnames".
