There's not really a lot you can do about someone copying your name - just be flattered I guess
But there's a lot you can do to manage your branding. Be active on social media and get as many likes and reviews as you can. Also beef up your Google Business listing by having awesome content and original photos and getting lots of 5 star reviews to make sure you beat everyone else out of the water.
A good, well-written website, with lots of relevant information and optimised for search engines should help, keeping the competition at arm's length. A good SEO company should be able to get you ranking well so you can leave the others behind. These guys are lazy and unprofessional, otherwise they wouldn't be taking the easy option of ripping off someone who is successful. So do all the things that they aren't prepared to do.
Offline you can build your reputation by networking and being seen in your community.
Good luck - it's a real pain when others try to cash in on your success, but at least you're doing something right!