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Cognomen Ásbjörg (Ásbjörg ) , all over the world, is an extremely rare last name. Predominantly, Ásbjörg is the forename as well as the last name.
Asbjoerg, Asbjorg, and Asbjørg
Jónsdóttir, Magnúsdóttir, Björnsdóttir, and Kristinsdóttir