People like spas because they seem like retreats. They are a luxury item. You want to choose a name that says luxury, peace, and exclusivity. To find a good name, first reivew the names of current spas in your area. It's ok to have the same name as a spa that's far away, but you don't want a name that is too similar to an existing spa. You also want to be sure that your spa appeals to your target audience. Some will like alternative medicine, some want traditional.
I think it highly depends on exactly what tone you are trying to set with this business. When I hear "spa" I think of massage, facials, manicures, pedicures, etc. On the other hand, I've heard of some workout facilities refered to as health spas as well.
It might help you to google "health spas" in your area to get an idea of the types of names that catch your attention or ones that you particularly like. One trend in my area of health spa names suggests that the spa is a spiritual experience. Names like "Balance Day Spa," "Origins," and "Chakras" all tend to draw from an Eastern influence. I've been to several and my favorite is currently "Fire Salon and Spa."
I think you need to keep the name short, clean, and free of cliches. Most people associate a spa experience with wealth, taste, and culture. To me, the name should reflect those things.
A health spa's name would have to be something to lure customers into your place of business. It should bring to mind everything a health spa offers--relaxation, health, massage, and other spa services. You are trying to sell a state of mind--feelings of peace, stress-free from the workplace, a place to unwind. Names that come to mind include, Tranquillity, Nirvana, Mind and Body, Body and Spirit, etc. A name should evoke whatever it is your spa is primarily selling to the public. Relaxation Spa, Day-Cation Destination, Meditation Spa--all of these could be used to attract people to a place where they can leave their cares behind.
I wrote a business plan for a day spa a couple of years ago and my virtual spa was called Elysium, its a mythical afterlife the Greeks believed in where the righteous could live out a happy and contented life indulging in whatever made them happy. I always thought it was a good name. Good luck!