Cognomen Asmundur (Asmundur 
) , all over the world, is an extremely rare family name. Much more frequently, Asmundur is the forename as well as the last name.
Herman, Jonsson, Hilmisson, Sveinsson, Asmundsson, Bjornsson, Gudjonsson, Heinesen, Magnusson, Sandagerdi, Steinthorsson, Kristinsson, Gunnlaugsson, Johannesen, and Thorvaldsson