Þorsteinsson is an Icelandic patronymic, meaning son of Þorsteinn. In Old Norse and Icelandic names, the name is not strictly a surname as it is not a family name. Notable people with this name include:
Björn Þorsteinsson (born 1940), Icelandic chess player Indriði G. Þorsteinsson (1926–2000), Icelandic novelist and short-story writer Jón Dagur Þorsteinsson (born 1998), Icelandic footballer Klængur Þorsteinsson (1102–1176), Icelandic Roman Catholic clergyman; bishop of Iceland 1152–76 Magnús Þorsteinsson (born 1961), Icelandic businessman; chairman and boardmember of several large businesses Pétur Þorsteinsson (born 1955), Icelandic priest and neologist; leader of an Icelandic language movement Skúli Þórsteinsson (fl. 11th century), Icelandic poet and warrior Þorbjörn Þorsteinsson (died 1158), Orcadian (of Orkney) pirate Þorsteinn Þorsteinsson (1880–1979), Icelandic economist and Esperantist Þorsteinn Þorsteinsson (athlete) (born 1947), Icelandic athlete who competed in the 800 metres Þorsteinn Þorsteinsson (footballer) (born 1964), Icelandic footballer