This happened to me when I was starting out. I'd been going a few months as Simply Nails and then discovered a place in a nearby town had just started up under the same name, and had just put a banner up in their window (it was a tanning shop but the banner had Simply Nails on as the nail lady had just started there).
It bothered me so much. We were both one-man-bands, doubt she had registered at Companies House as a public limited company lol, I know I hadn't. I kept thinking, what if she was rubbish and people talked about her business, and people associated that with mine?
After about a week I decided to change names. I'd had business cards etc printed, also 2,000 leaflets, but I just bit the bullet and had them all printed again with the new name (which I prefer heaps btw!).
The punchline is that she was only there for about 6 months and then disappeared without trace!!
So I know exactly how you feel hun, it is really annoying, but not much you can do. I would change my name for the salon, especially if she is down the same road as you. hth x