I think the question does not give us enough information. Is the massage practice in premises that are atmospheric? Does the massage offer facials as well? The word salon derives from the the "gathering" originally taken from Italy into the French. Nowadays, and in general terms the public would identify the word salon as a place that has beauty treatments in their variety or a hairdressing salon. To involve the word salon call it a "Massage salon" meaning a massage gathering this might help the public to identify that there were an array of massages offered.
Unwind Milton Keynes offers beauty and body treatments I am called a 'Studio' as it is run from my home, I wondered if I should be a salon too, but decided against it because I didn't want to mislead any one by them perceiving I was a glossy shop...I do have a glossy studio though lol.
The meaning of the word salon is "gathering" taken from the Italians and filtered it through to the French. To call a place a massage salon would be appropriate just as beauty salon offer their treatments and hairdressing offer theirs. I feel the word salon has an extra impact on the public denoting somewhere that might be more than a practice and therefore having atmosphere.
Sure, a massage practice can EVOLE into a salon/spa, but unless and until there are actually other beauty services being offered at your business, then it is essentially NOT a salon/spa. I would think that your direction for your massage practice will ultimately determine how you should classify it? Do you plan to offer other beauty services in the near future?
If you are just offering massage and no other treatments, I think it would be better worded as a Therapy room/establishment otherwise when you use the world salon or spa it gives the impression that you offer other beauty treeatments