The language spoken by the Elves of Rivendell in J.R.R. Tolkien’s works is Sindarin.
Sindarin is one of Tolkien’s major Elvish languages. In Middle-earth’s history, it develops from the language of the Sindar, or Grey Elves, and becomes a widely used Elvish language in the later ages.
Rivendell is home to Elrond and many Elves, and Sindarin names and phrases appear throughout the stories connected with the refuge. Tolkien constructed Sindarin with a developed sound system, grammar, and historical relationship to other Elvish languages.
Quenya is another major Elvish language, associated especially with the High Elves and influenced by Finnish. It is not simply another name for Sindarin. Khuzdul is the secret language of the Dwarves, while the Black Speech is associated with Mordor.