We occasionally hear of twins, or even a single child, speaking a private language they’ve invented themselves and that only they understand — a phenomenon known as idioglossia.
Certain brain injuries or neurological conditions can result in another form of idioglossia, where a person's speech becomes so distinct and full of mispronunciations that it's unintelligible to others, sounding like a different language. The word idioglossia comes from the Greek idioglossos, meaning "of a unique language," from idio-, "unique" and glossa, "language." A related word is idiolect, an individual’s personal, unique version of a language. Everyone speaks a slightly different idiolect of their native tongue.