It is possible to use multiple types for a single entity (i.e., Person and Organization), but I think it wouldn’t make sense in such a case. I’d argue that the business and the person running the business are different entities, even if they share the name.
Possible cases that make clear why having separate entities would be useful: the business might get a new name in the future, but the person will likely keep the name; the business might be sold, but not the person; etc.
You could provide both entities and relate them with the founder property.
Example in RDFa:
<div vocab="http://schema.org/" typeof="Organization">
<div property="name">John Doe</div>
<link property="url" href="/shop" />
<div property="founder" typeof="Person">
<div property="name">John Doe</div>
<link property="url" href="/" />
</div>
</div>
If the site has a page about the person (I assumed it’s the homepage in the example above) and about the business, you can use these URIs to identify the entities and reference them where needed (so you don’t have to duplicate the data about the person/organization on every page). In RDFa, the resource attribute can be used for this purpose.
Unless you provide irrelevant information (as in: spamdexing) in your structured data, there’s no reason to assume that it could affect your ranking.
