Since we're taking a little tour around the naming conventions of the world, this seems like a good moment to mention that Russian names too have traditionally relied on a patronymic naming system, e.g. Aleksandr Sergeyevich Pushkin's father was named Sergei.
All his children would thus have borne his first name as their patronym (Sergeyevich for boys, Sergeyevna for girls).
In Denmark, a different patronymic format was used in which, until the naming system was reformed in the 19th century, the father's first name became his offspring's surname. For instance, Peder Jensen's children might have been called Hans, Ole and Gerda Pedersen. Hans and Ole's children would have respectively Hansen and Olsen as their surnames, and their sister Gerda's children would have borne a surname formed from her husband's father's first name.
Not surprisingly, this convention has made tracing family lineages in Scandinavia quite a complicated undertaking, especially since the traditional repertoire of names in an overwhelmingly agrarian society was pretty limited in the first place.
Reply from Erik Kowal ( - England)