Family name Ingibjörg (Ingibjörg 
, Ingibjoerg ) , throughout the world, is an extremely rare cognomen. Much more frequently, Ingibjörg is the forename as well as the last name.
Ingadóttir, Jóhannesdóttir, Jóhannsdóttir, Einarsdóttir, Eiríksdóttir, Hinriksdóttir, Hjartardóttir, Friðriksdóttir, Þórðardóttir, Þorsteinsdóttir, Stefánsdóttir, Baldursdóttir, Ragnarsdóttir, Gunnarsdóttir, Gunnlaugsdóttir, Guðmundsdóttir, Haraldsdóttir, Halldórsdóttir, Valgeirsdóttir, Sigurðardóttir, Sigurjónsdóttir, Benediktsdóttir, Gísladóttir, Reynisdóttir, Bjarnadóttir, Björnsdóttir, Smáradóttir, Skúladóttir, Pálmadóttir, Pálsdóttir, Jónsdóttir, Elíasdóttir, Helgadóttir, Magnúsdóttir, Sigfúsdóttir, Sveinsdóttir, Kristinsdóttir, Snorradóttir, Jónasdóttir, Tómasdóttir, Hreiðarsdóttir, Frostadóttir, Árnadóttir, Óskarsdóttir, Ólafsdóttir, Þórisdóttir, Sverrisdóttir, Bernhöft, Karlsdóttir, and Kristjánsdóttir