The names in the poem are Celtic.  "Shalott," says Professor Rhys, of Oxford, is identical with "Escalot," or "Astolat;" and the original of this name, he thinks, is probably Alclut,—the old Welsh name of the rock of Dumbarton, in the Clyde, near Glasgow.*...
    * Professor Rhys is an authority, and not to be questioned.  But I had hitherto supposed "Shalott" to be the same word that we still have in "shallot," or "shalot," a kind of onion, from the Latin ascalonia, a shallot, the feminine of Ascalonius, belonging to Ascalon, a city in Palestine,—through the Old French eschalote, or eschalotte.  The form eschalote is a variant, or corruption, of the Old French escalogne, a shallot.  The Latin form is not final: back of it, there is the Greek Ασκάλων. (Vide Skeat's Etymological Dictionary, s. v. shallot, shalot.) (Poet Lore, v.4, 1892)

The Lady of Shalott.

Who is this? and what is here?
And in the lighted palace near
Died the sound of royal cheer;
And they crossed themselves for fear,
All the knights at Camelot:
But Lancelot mused a little space;
He said, "She has a lovely face;
God in his mercy lend her grace,
The Lady of Shalott."

    Shalott:  Tennyson apparently softened the name Astolat into this form.  One legend places it in Surrey, another on Dumbarton Rock in Scotland. (Jones Readers by Grades, Jones, v.8, 1904)

... Now speak we of the fair maid of Astolat, which made such sorrow day and night, that she never slept, eat, nor drank; and always she made her complaint unto Sir Launcelot.  So when she had thus endured about ten days, that she felt that she must needs pass out of this world.  Then she shrove her clean and received her Creator; and ever she complained still upon Sir Launcelot.  Then her ghostly father bade her leave such thoughts.  Then said she, "Why should I leave such thoughts? am I not an earthly woman? and all the while the breath is in my body I may complain.  For my belief is that I do none offense, though I love an earthly man; and I take God unto record, I never loved any but Sir Launcelot du Lake, nor never shall; and a maiden I am, for him and for all other.  And sith it is the sufferance of God that I shall die for the love of so noble a knight, I beseech the high Father of heaven for to have mercy upon my soul; and that mine innumerable pains which I suffer may be allegiance of part of my sins.  For our sweet Savior Jesu Christ," said the maiden, "I take thee to record, I was never greater offender against thy laws, but that I loved this noble knight, Sir Launcelot, out of all measure; and of myself, good Lord!  I might not withstand the fervent love, wherefore I have my death."... (The Warner Library, Cunliffe, v.6, 1917)