The origin of the name Kven is unclear. The name appears for the first time in a 9th-century Old English version, written by King Alfred of Wessex, of a work by the Roman author Orosius, in the plural formCwenas. Today, however, Kven refers to Finnish-speaking people who have migrated to northern Norway in relatively recent times, with no connection to the Cwenas/Kænir mentioned in the sagas.
Norwegian background
All ancient references to Kvenland and Kvens seem to be from Old English and Icelandicsources. Furthermore, most of them seem to have been connected to a certain geographical area in Norway in one way or another:
Egil's saga described how Thorolf travelled from Namdalen to Kvenland
Writer of the publication mentioning Terra Feminarum was especially familiar with Trondheim and also mentioned Hålogaland
Kvens were mentioned 1271 to have pillaged Hålogaland
This might indicate that the term Kven was originally used in Norwegian dialects around a rather compact area ranging from Trondheim to Hålogaland.
Theories
Widely accepted is the view first presented by Jouko Vahtola that kvenetymologically originates from Old Norsehvein, meaning "swampy land." Nevertheless, kven translates to "woman" in Old Norse. Proto-Germanic *kwinōn, *kunōn; *kwēni-z, *kwēnō "woman" developed into Old Norse kona; kvǟn, kvān, kvɔ̄n; kvendi; kvenna, kvinna. A reference to Terra Feminarum in a Latin text dated to 1075 CE is likely a translation of Kvenland. A 14th-century Icelandic manuscript describes a kuenna land north of Indiapopulated by hermaphroditic women.
Theory three: Sami background
Similar sounding words to "kainuu" also exist in the Sami languages. In Northern Sami, Gáidnu is a rope made of roots for boats or fishing nets. Gáidnulaŝ refers to a clumsy person and Geaidnu stands for a road or a way. In the early saami dictionaries Kainolats/Kainahaljo had the meaning Norwegian or Swedish man while Kainahalja had the meaning Norwegian or Swedish women, it could also have the meaning peasant. Helsing-byn close Torneå was referred to as Cainho.