@susanavello, @mike-stelzner @caseyvalianthas have very valid points. We had a client recently with a branding issue. He is a vocal coach so branding his name was important, but he had a new book coming out with a website named after it, so the book branding needed to also be pushed. We used both for obvious reasons already mentioned and since he had domain names for both, we just utilized them to promote his book website for better SEO. In our case, this person benefited from our expertise, but it really depends on your long-term goals.
Unless there is a very good reason to do so, I always suggest a formal (be sure it is unique, easy to spell and say) biz name and a DBA to start with and then expand from there. You want room for your biz to grow bigger than you ever anticipated so that others can help you run it, or sell it outright and start another biz.