General:
* Massage therapist
* Bodyworker
* Somatic practitioner
* Massage technician
* Massage specialist
More Specific:
* Sports massage therapist
* Swedish massage therapist
* Deep tissue massage therapist
* Prenatal massage therapist
* Reiki practitioner (if they also practice Reiki)
Informal:
* Masseur (male)
* Masseuse (female)
The best word to use will depend on the specific context and the type of massage being offered.