Idioglossia refers to an idiosyncratic language, one invented and spoken by only one or a very few people. Most often, idioglossia refers to the private languages of young children, especially twins. It is also called twin talk or twin speech. Children who are exposed to multiple languages from birth are also inclined to create idioglossias.
From Wikipedia, might be handy:
Idioglossia refers to an idiosyncratic language, one invented and spoken by only one or a very few people. Most often, idioglossia refers to the private languages of young children, especially twins. It is also called twin talk or twin speech. Children who are exposed to multiple languages from birth are also inclined to create idioglossias.