How about not using the term "psychiatric", "emotional" or "therapeutic." Simply "Medical Assist Service Dog." They are not allowed to ask the nature of the disability (severe psychiatric disorders, by the way are MEDICAL) - they just may ask what the animal is trained to do for you. Some give the pat answer of "ameliorate my medical disability." If necessary talk about alerting to medical episodes, or whatever.

Therapy dogs are NOT protected under the ADA. Just Service dogs. Medical vs emotional. Here's a book.

Many medical conditions are "invisible" - such as epilepsy, meniere's, fragile bones, hearing loss, episodic fluctuations in blood pressure, heart conditions, and more. They are not allowed to ask the diagnosis.