Iceland shares a common cultural heritage with the Scandinavian states of Norway, Sweden, and Denmark. Unlike those other nations, Icelanders have continued to use the old-style Scandinavian names, formerly used in Scandinavia but replaced by surnames in recent centuries. In the Icelandic system, there are no actual family names or surnames. A person's last name indicates the first name of the subject's father (or mother in some cases), that is, it is a patronymic (or matronymic). Family names exist in Iceland, and some while ago they existed as traditional surnames which are inherited through generations, but in today's Iceland they are technically middlenames, followed by the parent's first name.

For example, a man named Jón Stefánsson has a son named Fjalar. Fjalar's last name will not be Stefánsson like his father's; it will become Fjalar Jónsson, mentioning literally that Fjalar is the son of Jón.

The same goes for females. Jón Stefánsson's daughter Kata would not have the last name Stefánsson; she would have the name Jónsdóttir. Again, the last name literally means "Jón's daughter".

The vast majority of Iceland carries the name of the father, but in some cases the mother's name is used, for various reasons. Sometimes either the child or legal parent wishes to end social ties with the father, some feminists use it as a statement, and yet others simply find it a matter of style and nothing more. In that case, the convention is entirely the same. Fjalar, the son of Bryndís, will have the full name of Fjalar Bryndísarson (literally meaning "the son of Bryndís").

Foreigners often find it strange that Icelanders formally address others by their first name. For example, current prime minister Halldór Ásgrímsson would not be addressed as Ásgrímsson by another Icelander; he would either be addressed only by his first name (or first and second if he had one), or his full name. The cultural meaning of an Icelander's last name is not that it's a part of one's name, but a short description of who one is. Halldór is Ásgrímsson - a son of Ásgrím. Legally it is a part of his name. Culturally it is a definition of from whom he was begotten, even if that definition is seemingly vague.

One logical consequence of this is that in Iceland, directories of people's names, such as the phone directory, are alphabetized by given name, not by surname.

Another good example of the formal mode of address is the Icelandic singer and actress Björk. Björk is commonly mistaken for an artist's name or an artist's expression, such as "Sting". However, Björk is simply Björk Guðmundsdóttir's first name, as any Icelander would address her, whether formally or casually.

As a result, in a four-person family there might be four different last names: the married couple Jón (Stefánsson) and Bryndís (Atladóttir), and their children Fjalar (Jónsson) and Kata (Jónsdóttir). This also means that names of children do not necessarily reflect the marital status of their parents. Icelandic families have supposedly had difficulties with the customs services of foreign countries mistakingly believing their children may be being kidnapped because of the differing names. In more traditional countries or establishments it can also be fairly embarrassing for a person to check into a hotel with his or her spouse only to have to prove his or her marital status, though this has obviously become a less common requirement in recent decades.