echolalia

echolalia \ek-oh-LEY-lee-uh\, noun:

1. The imitation by a baby of the vocal sounds produced by others, occurring as a natural phase of childhood development.
2. Psychiatry. The uncontrollable and immediate repetition of words spoken by another person.

At the time when speech is being learned, there begins a period of echolalia in which the child repeats with tireless continuation all the words or sentences it hears; either completely, or else their closing cadences.
-- Kurt Koffka, The Growth of the Mind: An Introduction to Child Psychology

These "terrestrial echoes" where the "swamp's echolalia," according to Kiwi, who liked to make geography as pretentious as possible.
-- Karen Russell, Swamplandia!

I had cultivated a mild sort of insanity, echolalia, I think it's called. All the tag ends of the night's proofreading danced on the tip of my tongue.
-- Henry Miller, Tropic of Cancer

Echolalia originates from two Greek roots: echo derived from the name of the mythic nymph Echo fabled to have pined herself away to nothing but her name, combined with lalia meaning "talk or prattle."