This is an Icelandic name. The last name is a patronymic, not a family name; this person is properly referred to by the given name Thorvald, Thorvaldr, Þorvaldr or Þorvaldur.
Probable route of travel from Greenland to Vinland
The Greenland Saga describes a voyage made by Bjarni Herjolfsson, and the subsequent voyages of Leif Eriksson, his brother Thorvald Eiriksson, his sister Freydís Eiríksdóttir, and the Icelandic merchant Thorfinn Karsefni. The Saga describes hostilities with skraelings, the Norse term for the native peoples they met in the lands visited south and west of Greenland which they called Vinland and Markland. The Saga of Erik the Red tells the story as a single expedition led by Thorfinn Karsefni. The voyage of Thorvald Eriksson is told here as part of the Karlsefni expedition. [2]
Haugen, Einar (2007) Voyages To Vinland - The First American Saga Newly Translated And Interpreted (Barzun Press) ISBN 978-1406774993
Jones, Gwyn (1986) The Norse Atlantic Saga: Being the Norse Voyages of Discovery and Settlement to Iceland, Greenland, and North America (Oxford University Press) ISBN 0-19-285160-8