[1] The name stems from Guðrún Ósvífrsdóttir, who is a main character in Laxdæla saga.
In Laxdæla saga Guðrúnarlaug (literally "Guðrún's pool" in Icelandic) is called "the Baths of Saelingsdale": Gestur ríður nú um daginn vestan úr Saurbæ og kemur til Sælingsdalslaugar og dvelst þar um hríð.
Guðrún kom til laugar og fagnar vel Gesti frænda sínum.
kafli Now Guest rideth westward all day from Saurby and cometh to the Baths of Saelingsdale, and abides there awhile.
Guest took her greeting well, and they fall to speech together, for both of them were wise and many-spoken.