Cryptophasia
Cryptophasia is a phenomenon of a language developed by twins (identical or fraternal) that only the two children could understand. The word has its roots from crypto meaning secret and phasia meaning speech. Most linguists associate cryptophasia with idioglossia, which is any language used by only one, or very few, people. Cryptophasia also differs from idioglossia on including mirrored actions like twin-walk and identical mannerisms.