Branding is a personal thing. I see people in business who think their business or product is the brand. No, the person in the business is the brand.
What you say, how you say it, your value, customer value, your service, the experience of everyone that comes to you, how you impact, influence or talk to people... all these are what makes your brand. Branding is personal.
Yeah, we individually are a brand and whatever we do as individuals or as a business entity contributes or take away from the brand. It is actually more than the name but the experience the business give.