Gestsson is a patronymic (see Icelandic name). Notable people with the patronymic include:
Auðunn Gestsson (1938–2020), Icelandic newspaper salesman Pálmi Gestsson (born 1957), Icelandic actor and voice actor Svavar Gestsson (1944–2021), Icelandic politician Teitur Gestsson (born 1992), Faroese football goalkeeper