I agree with not changing the name of the business. You need as much transparency as you can manage while keeping yourself out of legal hot water. You don't want customers to be in a position of wondering "if". As much as possible while keeping yourself out of potential legal trouble, you need to demonstrate that YOU are: honest, saddened / horrified / shocked / embarrassed by the situation (whichever fits and is your honest emotion, without getting yourself into legal trouble), what steps you've taken, what steps you're taking going forward, that you're understanding of those customers who've chosen not to continue with you, and that you're deeply appreciative of the customers who stay.

Be sure to quietly seek the advice of a good attorney and have them OK all your statements before you put them out there. But make sure YOU actually write them so they don't sound like canned statements. With your attorney's permission, let your customers in on what steps you've taken so far (fired the employee?placed them on unpaid leave pending a thorough investigation?) and what specific steps you're taking going forward (Extensive new types of background checks and personality tests? New security procedures? Or whatever fits the situation).

Meanwhile, focus your attention on the customers who stay loyal. Thank them with some sort of special discount or offer--but do it carefully and with a deeply grateful and appreciative tone, rather than a bright and chirpy tone. Maintain a list of those who stay with you through this, and continue to remember and reward them in the future after the storm is past.

Your tone is everything in this matter. Never say "no comment" to a reporter. (Google "alternatives to saying no comment"--there are many.) Do not let your customers or the public see you be defensive or angry. They need to see you being a pro-active leader who recognizes the seriousness of the situation. It's over-used, but you really do need a tone of resolute "keep calm and carry on."

If you try to hide or pretend nothing happened, it will backfire.

Good luck, and feel free to call me to explore more ideas or develop a specific strategy.