The Secretary of State (or local county clerk) is responsible only for ensuring that names are not identical -- and "Flutter" is not identical to "Salon Flutter."
There are a couple of ways you can approach this. First, you can consult with an attorney to see if there are any state trademark bases for getting the other company to change its name.
Second, you'll want to find out from customers whether there's been any confusion about who's handling eyelash extensions.
Finally, from a marketing perspective, it may be worth exploring with them whether they really intend to offer the full range of services you do. If not, you may find that the company you thought was a competitor could become a strategic ally.
Nina L. Kaufman, Esq. is an award-winning New York City attorney, edutainer and author. Under her Ask The Business Lawyer brand, she reaches thousands of entrepreneurs and small business owners with her legal services, professional speaking, information products, and LexAppeal weekly ezine. She also writes the Making It Legal blog.