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Around the globe, Ásgrímsson (Ásgrímsson ) is an extremely rare unknown gender first name. Much more prevalently, Ásgrímsson is the last name as well as the forename.
Asgrimsson
Kári, Páll, Stefán, Davíð, Halldór, Ásgrímur, Ísleifur, Sigurður, Aðalsteinn, and Guðmundur