Companies are like a group of people lead by a person who is often called as CEO of the company. In a small business, the owner often does most of the work, right from a lower level employee to the highest level executive.
In other words, a small business owner is the lifeline of his or her business. Unless one employs thousands of employees, he or she is a small business owner. She thus is the reason that business exists. It is often the case that small business owner would like customer to know her business by business name rather than her own name.
As noble as it sounds, in my opinion it is not the best strategy. In case of small business, personal relations and credibility are far more important than the business name. Of course building a great brand is necessary but till the time the business reaches such a stage, business owner name sounds more credible.
Customers of small business owners would like to reach out directly to the business owner in case they face any issue rather than waiting on a phone line. They would like to speak to someone important. It is not possible to do this in large business. The personal touch is missing over there.
A small business's success is completely dependent on how much familiar their customers are with the business owner. It is in the interest of business owner too to put herself above her organization, at least till the time business grows so much that ultimately the brand becomes bigger than the person itself.
Till that time you are above your business.