I usually look at individual names vs business names as who is doing the work, or who am I working directly with (for the most part). If you look at hair stylists, gym trainers, chiropractors etc, you're usually looking at a name. If you're dealing with a team of people, you'll probably have a business name.
Not always true, as you get people like "Tony Robbins," where everything is built around the one person and his philosophy, but you're usually only dealing with his team and never him directly.
Personally, I prefer business names or descriptive names. It leaves room for business expansion and the ability to sell the business and have an exit strategy. There's a big difference between lance-yang.com, and the-lance-yang-method.com or the-yang-group.com. It's all about the exit strategy and the legacy after the head person steps down.
The Ford Modeling Agency (operated by Eileen Ford, pretty much fell apart as the business was based around her name and her talent and creative style. It's still around, but doesn't carry the same weight.
That said, nobody can deny that the "Walt Disney Productions" continued to survive after the namesake died 🙂