The fictional language Tolkien developed as the speech of the Grey-elves is Sindarin.
Sindarin is one of Tolkien’s principal Elvish languages in Middle-earth. It was spoken by the Sindar, or Grey-elves, who remained in Beleriand after the other Teleri traveled toward the West. Tolkien based much of Sindarin’s sound and historical development on Welsh, while Quenya drew more strongly on Finnish and Latin influences.
Sindarin became a common Elvish language in much of Middle-earth during the later First Age and the Second and Third Ages. Names such as Rivendell, Lothlórien, and Moria are associated with Tolkien’s invented linguistic traditions, although names in Middle-earth can derive from several languages.
Quenya is a different Elvish language, associated especially with the High Elves and influenced by Tolkien’s interest in Finnish. Westron is the Common Speech of many peoples, while Khuzdul is the secret language of the Dwarves.