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Last name Þórður (Þórður ) , globally, is an extremely rare cognomen. Much more frequently, Þórður is the forename as well as the last name.
Mar, Jörundsson, Einarsson, Hjörleifsson, Fjalarsson, Ólafsson, Þórisson, Þorvaldsson, Þorsteinsson, Sigurðsson, Stefánsson, Pétursson, Guðmundsson, Jóhannesson, Júlíusson, Halldórsson, Vilmundarson, Friðriksson, Friðjónsson, Ásgeirsson, Ragnarsson, Þórðarson, Guðjónsson, Guðlaugsson, Reimarsson, Kárason, Ólason, Möller, Atlason, Bogason, Pálsson, Jensson, Jónsson, Harðarson, Ingason, Oddsson, Kristleifsson, Ulfarsson, Ásmundsson, Magnússon, Sturluson, Sveinsson, Baldursson, Bragason, Birgisson, Björnsson, Bjarnason, Karlsson, Árnason, and Kristjánsson