idioglossia

idioglossia\ id-ee-uh-GLOS-ee-uh \ , noun;
1. A private form of speech invented by one child or by children who are in close contact, as twins.
2. A pathological condition in which a person's speech is so severely distorted that it is unintelligible.

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Or, maybe how we Texans talk. For example, in Tex-speech, my sister Sharon's name is pronounced "Shurren".