Idioglossic

An idioglossia is an idiosyncratic language invented and spoken by only one person or very few people. Most often, idioglossia refers to the "private languages" of young children, especially twins, the latter being more specifically known as cryptophasia, and commonly referred to as twin talk or twin speech.

Children who are exposed to multiple languages from birth are also inclined to create idioglossias, but these languages usually disappear at a relatively early age, giving way to use of one or more of the languages introduced.

...
Wikipedia