Aside from the legalities that "may" arrise, it sounds like this is sort of a newer business?
If so, remember, that other place with same/similar name might have a less than stellar reputation, so you don't want people associating you with them
On the other hand, if they are the best thing since sliced bread.....
You see where I'm going. Get your own DISTINCT name and kick some bootie!
Best of luck, Bryan