If you have a one-person business, there are two ways that you can go about branding yourself.
You can brand yourself as just yourself, and create a logo based on just your name and your personality. The advantage to this is that the business brand can be very tied to you – which means that your customers will typically expect to have you involved directly in their accounts and possibly even the day-to-day management of their projects.
Or, you can brand yourself as a larger business entity. In this type of brand, you typically give your company its' own name and concentrate on separating your personality from the company's. This can help you manage customer relationships, and can also help your company grow later on. But, it can take more soul-searching and work to initially set up.