What is a person who gives a massage called?

In the old terminology:

A woman who gives massages professionally is called a masseuse.

A man who gives massages professionally is called a masseur.

Today, however, the term Massage Therapist is the best Word describe a person who performs Massage Therapy.

A masseuse or masseur is generally associated with an untrained person giving massages that often include sexual acts. A massage therapist has completed massage therapy training and in most states is required to be licensed (they will be listed as an LMT in any advertisements.)