Surname Ásgrímur (Ásgrímur 
) , across the world, is an extremely rare family name. Much more prevalently, Ásgrímur is the forename as well as the last name.
Logason, Jónasson, Einarsson, Ásgrímsson, Sigurðsson, Stefánsson, Albertsson, Guðmundsson, Hermannsson, Friðriksson, Gunnarsson, and Gudmundsson