There are laws that govern various States that are limiting or deciding the terminology and criteria for the terminology. When using the term hypnotherapy it is implied that the hypnotist may be engaging in psychotherapy, which is not the case.
The National Guild of Hypnotists is encouraging all of its members to use the title of "Hypnotist" in all cases.
I use the NGH recommended title of "Consulting Hypnotist". The official definitions of Consulting Hypnotism approved by the National Guild of Hypnotists are “Consulting Hypnotists help ordinary people with ordinary, everyday problems using individual hypnotic techniques” for practitioners, and “Consulting Hypnotism is motivational coaching by means of hypnotism”.
I practice in the State of Washington where I am considered a "Hypnotherapist". In order to practice in Washington State we have to obtain a "Hypnotherapist Registration".
I am also a member of the IAHP (International Association of Hypnosis Professionals) and my preferred designation is "Certified Hypnosis Professional". This designation is approved by the NGH.