Origin of the name Kven
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 form "Cwenas". It is still in use today, indicating a Finnish speaking Kven minority in northern Norway.
All ancient references to Kvenland and Kvens seem to be from Old English and Icelandic sources (9th to 13th centuries). Furthermore, most of them seem to have been connected to a certain geographical area in/and or near the modern-day area of Norway in one way or another:
- Ohthere of Hålogaland, the source used by King Alfred of Wessex, was from Hålogaland.
- Orkneyinga saga describes how Nór travelled from Kvenland to Trondheim.
- Egil's Saga describes how Thorolf travelled from Namdalen (north of Trondheim) to Kvenland.
- Writer of the publication mentioning Terra Feminarum was especially familiar with Trondheim, and the writer also mentions Hålogaland.
- In 1271, Icelandic annals report the following to have happened in Norway: "Then Karelians and Kvens pillaged widely in Hålogaland."
Possibly, this might suggest that the term "Kven" was originally used of the Finnic neighbors of the ancient inhabitants of the modern-day area of Norway. As Hålogaland is suggested to have been the first kingdom in what today is Norway, and since the above medieval references to the Kvens all pertain to a rather compact area, ranging from Trondheim to Hålogaland and some of the surrounding territories, it is possible that the term Kven derives from an ancient language or dialects spoken in the modern-day area of Norway, possibly first in the middle to northern parts of it.
Theory one: "Swampy land"
Widely accepted is the view first presented by Jouko Vahtola that "kven" etymologically originates from Old Norse "hvein," meaning "swampy land". If Kvenland was the same as Finland and since Finland of the past consisted largely of swamp lands, the theory would fit.
In medieval accounts, Kvenland is presented as the "land of the Kvens". The terms Kven and Kvenland can be found mainly from Icelandic accounts. A Norwegian adventurer and traveller named Ohthere visited England around 890 CE. King Alfred of Wessex had his stories written down, and included them in his Old English version of a world history written by the Romano-Hispanic author Orosius. Ohthere's story contains the only contemporary reference to Kvenland that has survived:
[Ohthere] said that the Norwegians' (Norðmanna) land was very long and very narrow ... and to the east are wild mountains, parallel to the cultivated land. Sami people (Finnas) inhabit these mountains ... Then along this land southwards, on the other side of the mountain (sic), is Sweden ... and along that land northwards, Kvenland (Cwenaland). The Kvens (Cwenas) sometimes make depredations on the Northmen over the mountain, and sometimes the Northmen on them; there are very large [freshwater] meres amongst the mountains, and the Kvens carry their ships over land into the meres, and thence make depredations on the Northmen; they have very little ships, and very light.
Kvenland can also be found used as a geographical term in some medieval accounts. It appears e.g. once in a list of countries found in Leiðarvísir og borgarskipan, which was basically a guidebook for pilgrims about the routes from Northern Europe to Rome and Jerusalem, written by an Icelandic Abbot Níkulás Bergsson in the monastery of Þverá (Munkaþverá) in the late 1150s CE. The publication contains two descriptions of lands around Norway that the Abbot seems to have acquired for his book from independent sources.
Götaland (Gautland) is east of the River Göta (Gautelfi), and closest to it is Sweden (Svíþjóð), then closest is Hälsingland (Helsingaland), then Finland (Finnland); then come the borders of Russia (Garðaríki), which we mentioned earlier. But on the other side of Götaland is Denmark.
Closest to Denmark is little Sweden (Svíþjóð), there is Öland (Eyland); then is Gotland (Gotland); then Hälsingland (Helsingaland); then Värmland (Vermaland); then two Kvenlands (Kvenlönd), and they extend to north of Bjarmia (Bjarmaland). From Bjarmia, uninhabited lands stretch in the north to the borders of Greenland (Grænland). 
Theory two: "Woman"
Whatever the origin of the name "kven" is, it resembles the Old Norse word for "woman" . Proto-Germanic "*kwinōn, *kunōn; *kwēni-z, *kwēnō" for "woman" had developed into "kona; kvǟn, kvān, kvɔ̄n; kvendi; kvenna, kvinna" in Old Norse. An example of this is that Kvenland was most likely referred to as Terra Feminarum ("Woman Land" or "Land of Women") in a Latin text from 1075 CE. In this occasion, the term Finland is not mentioned.
Another reference to a north-bound land of women is from an Icelandic manuscript from the 14th century that describes a kuenna land ("Woman Land") north of India that would only have women with both reproduction organs. As the name appears in a geographical list of countries and Finland is nowhere to be found, it may also be a misunderstanding from an era that no longer recognized Kvenland any more.
The reason why Finland would have been called as "Woman Land" is not immediately explained. However, there was a rumour already in the 1st century CE, written down by Tacitus himself, that a tribe called Sitones possibly living somewhere in the present-day area of Finland and some of the surrounding areas was ruled by a woman. This could have led into some Germanic tribes calling Finland as the "Woman Land".
As a name for a country, Kvenland seems to have gone out of ordinary usage around the end of the Viking Age, unrecognized by scholars by the 14th century. As the first ever account written in Swedish language, Eric's Chronicle, was published as late as the 14th century, no medieval references to "Kvenland" or "Kvens" are available from Swedish literature.
All in all, there was a persistent tradition of various contents about a land controlled by women in the north which might have generated the name "Kvenland" in a somewhat similar manner than later times invented the name for the River Amazon.
One possibility is that "kven" is not originally a Germanic word at all, but lifted from Finnish. However, no fitting etymology has been presented for this theory.
Related to the discussion around the origin of the name Kven is also the origin of the name Kainuu.
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.
- Vahtola, J. (1994), Kvenerne – vem var de ursprungligen? In: Torekoven Strøm (eed.), Report from the seminar ”Kvenene – en glemt minoritet?” 14.11.94 at the University of Tromsø/Tromsø Museum.
- Vahtola, J. (2001), Folk och folkgrupper inom det nordliga rummet över tid. In: Tedebrand, L.-G. & Edlund, L.-E. (ed.), Tre kulturer i möte. Kulturens frontlinjer. Papers from the research program Kulturgräns norr, 27. Published by Johan Nordlander-sällskapet, 23. Umeå.
- Etymology of hvein.
- Online edition of Ohthere's description of Kvenland. A more faithful edition of the original text is in Thorpe, B., The Life of Alfred The Great Translated From The German of Dr. R. Pauli To Which Is Appended Alfred's Anglo-Saxon Version of Orosius, Bell, 1900, pp. 250-52. Note that in translations here the names of places, countries and people have been harmonized to forms used in Wikipedia, while forms used in the text are presented in parentheses.
- Given the context, "geond", with a range of possible meanings in "throughout", "over" and "as far as", is best understood as "amongst"; and "moras", with a range of possible meanings in "moors" or "mountains", is best understood as "mountains", though "moors" may be intended. The word mór  m (-es/-as) used in the original text can be translated as moor, morass, swamp; hill, mountain. See e.g. .
- Rafn, C. C. Antiquités Russes II, pages 404-405. Translation provided here is by the author of the article.
- Etymology of kwen.
- Manuscript "AM 764 4to". See also entire text in Icelandic.
- Kyösti Julku: Kvenland - Kainuunmaa, page 51. With English summary: The Ancient territory of Kainuu. Oulu, 1986.
- Tacitus' Germania.
- Korhonen, Olavi: "Håp - vad är det för en båt? Lingvistiska synpunkter. Bottnisk kontakt I. Föredrag vid maritimhistorisk konferens i Örnsköldsvik 12-14 februari 1982. Örnsköldsvik 1982."
- Lexicon lapponicum, Erik Lindahl, Johann Öhrling, Typis Joh. Georg. Lange, 1780"