Tolkien believed he had invented the word hobbit. He was probably right about his own mind and wrong about the language.
His own account is famous. Recalling a moment around 1930, he said he was grading exam papers and found a blank page. On it he wrote, "In a hole in the ground there lived a hobbit." Wordorigins.org cites a 1968 BBC interview for the story. He had told it before, in a 1955 letter to W.H. Auden quoted by Etymonline: "I did not and do not know why." The line became the opening of The Hobbit.
Tolkien later dressed the word in a history from inside his fiction. In Appendix F of The Lord of the Rings, he called hobbit a worn-down form of holbytla, "hole-builder," a word preserved more fully in Rohan. The parts are real Old English: hol, "hole," and bytla, "builder." The compound itself, the Oxford University Press blog notes, is not known to have existed. A real descendant would more likely have come out as hobittle.
Tolkien was less sure in private. The OED published its entry in a 1976 supplement. In a letter of 11 September 1970 he told its editors that his claim to the word was "not clear," and that he had not looked into it.
The surprise came in 1977, when The Times reported an earlier use. The Denham Tracts, a collection of northern English folklore gathered by Michael Denham, include "hobbits" in a long list of spirits and bogies. The OUP blog says the word first appears in the 1853 version of that list, and the Folklore Society reprinted it in 1895. In the list it sits just before hobgoblins.
That earlier hobbit was a kind of ghost, with no description. Etymonline adds that the name appears nowhere else in folklore. Wordorigins.org finds no evidence that Tolkien read the tracts, though he had access to them. Any borrowing, it suggests, was probably unconscious.
That stock is hob. Wordorigins.org says hob is most likely a nickname for Robert, and it turns up in hobgoblin and hob-thrush, names for household sprites. One more hobbit is unrelated: Etymonline records it in an 1835 court case as a Welsh measure of four pecks.