Legal Question in Intellectual Property in California

Re: Can they force to change my business name?

Yes. There are several grounds upon which you can legally keep your name. First, there is no certainty their trademark application will be granted. Common words, even foreign words, are often refused trademark protection because they are considered too generic and commonplace.

Next, trademark protection is somewhat line-of-business specific. You could have, for example, a red wine trademarked "Carmenet" which would preclude someone from trademarking a white wine Carmenet, but would not preclude using Carmenet as a paint color or for a perfume.

Third and finally, your name and the spa's name are not the same. The issue would then be whether there was a realistic possibility of confusion. Partially-overlapping names usually are considered sufficiently different so as not to create confusion, especially if neither name is a famous brand.

This is not to say they won't sue you, only to say that if they do you are likely to have one or more very solid defenses.

Re: Can they force to change my business name?

It partly depends on how they defined their Trademark application. If they were specific and their definition does not include your offered services then there are ways to strengthen your position. It would take knowing all of the details (i.e., seeing the letter, researching their trademark application) and coming up with a strategy.