[thristian]

Icelandic names follow that pattern. Björk's full name is "Björk Guðmundsdóttir" because she is the daughter of Guðmundur Gunnarsson.

English-speaking countries generally don't do that. For a long time people had only first-names, and disambiguated with nicknames or patronymic names where necessary. Eventually as society got larger and more complicated, governments started legally requiring people to have surnames, and they more or less stuck. If you meet a John Williamson today, his father probably isn't called William, but he's probably descended from a William who lived in the late medieval/early modern era.