Finnbogason is an Icelandic patronymic, meaning son of Finnbogi (= "Finn bow", "Finnish bow"). In Icelandic names the name is not a family name, but a patronymic. Notable people with the name include:
Alfreð Finnbogason (born 1989), Icelandic football striker Birgir Finnbogason (born 1948), Icelandic handball player Guðmundur Finnbogason (1873–1944), Icelandic philosopher; one of the first Icelandic psychologists Kjartan Finnbogason (born 1986), Icelandic football striker Kristján Finnbogason (born 1971), Icelandic football goalkeeper Kristján Flóki Finnbogason (born 1995), Icelandic football forward