Since it is an agency, as an organization cannot merely be run by an individual, even if one has a piece of complete knowledge. With the growing competition, what one needs to not just to survive the market but also lead it, needs a lot of input from specialized people. And, a branding agency is composed of is all those specialized individuals with expertise in their particular fields. The key players within a branding agency are defined by the tasks they are responsible for.
As a firm by the general rule, a branding agency can be run by a proprietor or can even be run by multiple people giving it partnership firm, private limited firm, public limited firm, etc, kind of constitution. A branding agency can even hire skilled freelancers to do the job.