Today the Lady of the Lake is best known as either Nimuë (Nimue), or several scribal variants of Ninianne and Viviane.
Medieval authors and copyists produced various forms of the latter, including Nimane (Vulgate Merlin, in addition to "Viviane"), Nimanne / Niv[i]en[n]e / Vivienne (Huth Merlin), Vivien, Vivian, Nimiane/Niniame (Arthour and Merlin and Henry Lovelich's English Merlin Continuation), Nymenche (Lancelot Propre), Nin[i]eve (Post-Vulgate Suite du Merlin), Niniane (Livre d'Artus), Niviana (Baladro del Sage Merlin), and Ui[n/ui]ane (Estoire de Merlin), among other variations, including alternate spellings with the letter i written as y (such as Nymanne or Nynyane).
The most primitive French form might be Niniane.
The form Nimue, in which the letter e can be written as ë or è, has been popularized by Thomas Malory's Le Morte d'Arthur and itself has several variations: in William Caxton's edition, her name appears as Nymue, Nyneue and Nynyue, but it had been rather Nynyve (predominantly) and Nenyve in Malory's original Winchester Manuscript.
Even though "Nymue", with the m, appears only in the Caxton text, Nimue is perhaps the most common form of the name of the character as this was the only version of Le Morte d'Arthur published until 1947.

Arthurian scholar A. O. H. Jarman, following suggestions first made by scholars of the 19th century, proposed that the name "Viviane" used in French Arthurian romances were ultimately derived from (and a corruption of) the Welsh word chwyfleian (also spelled hwimleian, chwibleian, et al.
in medieval Welsh sources), meaning "a wanderer of pallid countenance", which was originally applied as an epithet to the famous prophetic "wild man" figure of Myrddin Wyllt (a prototype of Merlin) in medieval Welsh poetry.
Due to the relative obscurity of the word, it was misunderstood as "fair wanton maiden" and taken to be the name of Myrddin's female captor.
Others have linked the name "Nymenche" with the Irish mythology's figure Niamh (an otherworldly woman from the legend of Tír na nÓg), and the name "Niniane" with either the Welsh mythology's figure Rhiannon (another otherworldly woman of a Celtic myth), the 5th-century saint Ninian, or the river Ninian.
Further theories connect her to the Welsh lake fairies known as the Gwragedd Annwn (including a Lady of the Lake unrelated to the legend of Arthur), the Romano-British water goddess Coventina (Covienna), and the North Caucasian Satanaya (Satana) from the Nart sagas.

Chrétien de Troyes's Lancelot, the Knight of the Cart, the first known story featuring Lancelot as a prominent character, was also the first to mention his upbringing by a fairy in a lake.
If it is accepted that the German Lanzelet by Ulrich von Zatzikhoven contains elements of a more primitive version of this tale than Chrétien's, the infant Lancelot was spirited away to a lake by a water fairy (merfeine in Old High German) known as the Lady of the Sea and then raised in her Land of Maidens (Meide lant).
The fairy queen character and her paradise island in Lanzelet are reminiscent of Morgen (Morgan) of the Island of Avallon in Geoffrey of Monmouth's Vita Merlini.
Guendoloena and Ganieda, respectively Merlin's one-time wife and his sister from Geoffrey's work, as well as the Roman goddess of the hunt and the nature, Diana, can also be considered prototypes.
Today the Lady of the Lake is best known as either Nimuë (Nimue), or several scribal variants of Ninianne and Viviane. Medieval authors and copyists produced various forms of the latter, including Nimane (Vulgate Merlin, in addition to "Viviane"), Nimanne / Niv[i]en[n]e / Vivienne (Huth Merlin), Vivien, Vivian, Nimiane/Niniame (Arthour and Merlin and Henry Lovelich's English Merlin Continuation), Nymenche (Lancelot Propre), Nin[i]eve (Post-Vulgate Suite du Merlin), Niniane (Livre d'Artus), Niviana (Baladro del Sage Merlin), and Ui[n/ui]ane (Estoire de Merlin), among other variations, including alternate spellings with the letter i written as y (such as Nymanne or Nynyane). The most primitive French form might be Niniane. The form Nimue, in which the letter e can be written as ë or è, has been popularized by Thomas Malory's Le Morte d'Arthur and itself has several variations: in William Caxton's edition, her name appears as Nymue, Nyneue and Nynyue, but it had been rather Nynyve (predominantly) and Nenyve in Malory's original Winchester Manuscript. Even though "Nymue", with the m, appears only in the Caxton text, Nimue is perhaps the most common form of the name of the character as this was the only version of Le Morte d'Arthur published until 1947. 
Arthurian scholar A. O. H. Jarman, following suggestions first made by scholars of the 19th century, proposed that the name "Viviane" used in French Arthurian romances were ultimately derived from (and a corruption of) the Welsh word chwyfleian (also spelled hwimleian, chwibleian, et al. in medieval Welsh sources), meaning "a wanderer of pallid countenance", which was originally applied as an epithet to the famous prophetic "wild man" figure of Myrddin Wyllt (a prototype of Merlin) in medieval Welsh poetry. Due to the relative obscurity of the word, it was misunderstood as "fair wanton maiden" and taken to be the name of Myrddin's female captor. Others have linked the name "Nymenche" with the Irish mythology's figure Niamh (an otherworldly woman from the legend of Tír na nÓg), and the name "Niniane" with either the Welsh mythology's figure Rhiannon (another otherworldly woman of a Celtic myth), the 5th-century saint Ninian, or the river Ninian. Further theories connect her to the Welsh lake fairies known as the Gwragedd Annwn (including a Lady of the Lake unrelated to the legend of Arthur), the Romano-British water goddess Coventina (Covienna), and the North Caucasian Satanaya (Satana) from the Nart sagas.
Chrétien de Troyes's Lancelot, the Knight of the Cart, the first known story featuring Lancelot as a prominent character, was also the first to mention his upbringing by a fairy in a lake. If it is accepted that the German Lanzelet by Ulrich von Zatzikhoven contains elements of a more primitive version of this tale than Chrétien's, the infant Lancelot was spirited away to a lake by a water fairy (merfeine in Old High German) known as the Lady of the Sea and then raised in her Land of Maidens (Meide lant). The fairy queen character and her paradise island in Lanzelet are reminiscent of Morgen (Morgan) of the Island of Avallon in Geoffrey of Monmouth's Vita Merlini. Guendoloena and Ganieda, respectively Merlin's one-time wife and his sister from Geoffrey's work, as well as the Roman goddess of the hunt and the nature, Diana, can also be considered prototypes.
Lady of the Lake