Ambiloquy is a rare word that refers to the ability to speak from both sides of the mouth at once. Due to its obscure nature, it may be difficult to find exact synonyms for ambiloquy. However, some words that are closely related to ambiloquy include equivocality, ambiguity, double speak, and ambidexterity in speech. These words imply a certain level of duality or double-sidedness in communication, which is a characteristic of ambiloquy. Other potential synonyms for ambiloquy could include deceptive speech, two-facedness, or even forked tongue, as all of these terms imply a certain level of insincerity or falsehood in one's speech.