Wow – Changing a name is a very big step.
Your name is your brand. Here is the definition of a brand from Wikipedia:
In marketing, a brand is the symbolic embodiment of all the information connected with a product or service. A brand typically includes a name, logo, and other visual elements such as images or symbols. It also encompasses the set of expectations associated with a product or service which typically arise in the minds of people. Such people include employees of the brand owner, people involved with distribution, sale or supply of the product or service, and ultimate consumers.
The only good reason to change your name is if the existing name has a poor brand identity. Changing the name is a way to wash the bad identity away. If you change the name for this purpose make sure you change as many other brand-related things as possible like the sign, logo, colors, uniforms, advertising and decor.
Being forced to change your name is another story entirely. Things like a name that is too close to another trademarked name or rebranding the store to leave a franchise organization may force you to rename a store.
You can minimize the damage to an existing satisfied customer base if you have a mailing list and use it to tell them about the name change.