Hi Ross,
That's a great question and exactly one of the reasons I was so stubborn on building a personal brand at first. I believed that if I used my personal brand to launch a business than one would never exist without the other. I believe I was wrong in that thought and missed out on opportunities because I wasn't ready for them.
I use one brand to boost the other. I'll use my personal brand to boost a product and a product to boost my personal brand but I always represent them as separate identities. They are individual brands because they act in their own regard and are always working on different projects within their specific industries. They are interwoven because you usually work with your own brands first.
One thing to keep in mind is that even though you are using your personal brand to boost your business, you want to make your business run without you as a person. The business can keep the brand, but it can't keep you.
For example if the only way you are taking payment is through email, invoice or cash, you want to look into an automated payment processor so you can still receive revenue without YOU actually taking it. Does that make sense?