The use of family names began in Iceland in the seventeenth and eighteenth centuries, and their number increased considerably during the nineteenth century. However, family names never came close to replacing the old custom of patronymics, which is still predominant in Iceland today: son (son) or dottir (daughter) is attached to the father's (or mother's) Christian name, e.g. Jon Einarsson, Helga Einarsdottir.

The Personal Names Act of 1913 gave statutory approval to the use of family names of the European model. However, 12 years later this policy was reversed. By the 1925 Personal Names Act, the adoption of new family names became illegal. However, those who had family names before 1925 could keep them, and they passed them on to their descendants, and wives can adopt their husband's family name (wives of husbands with the ordinary patronymic keep their own maiden patronymic; for practical reasons it is, however, permitted to enter the husband's patronymic in the wife's passport when going abroad).

People in Iceland with a family name are a small minority.  It should be noted that in Icelandic telephone directories one should, as a rule, look for the name of a person under the first letter of his Christian name. However, a person with a family name may be listed under the first letter of the family name.

According to present law (Personal Names Act, No. 37/1991) every Icelandic national shall have "one and up to three Icelandic first names". Foreign nationals shall adopt an Icelandic first name when they acquire Icelandic nationality and their descendants shall abide by the rule on patronymics.