To add to what FlyingRon has said, the entertainment business with the same name can assert their rights in the business name and is more apt to do this if the name is registered with the state of New Jersey and/or federally registered.
If the entertainment business has been using the name longer than you have and finds your use of the name confuses consumers into thinking you are affiliated with, endorsed by, sponsored by or in any way connected with their business when you aren't, you may find yourself with a legal challenge to your use of the name, especially if your fields of entertainment overlap. It will often be the first to use a name in commerce that will have greater rights to the name and can prevent the use of the name by others.
Facts matter, though. If you have been using your performance name publicly for some time without conflict, the entertainment business may not find your use infringing on any of their rights. You can check with an attorney in your area, though, for a better assessment of your legal risks.
Good luck.