Unfortunately at this time the answer is no. While having a profile is a requirement to getting your shop for free, we do not currently connect the two.
You can list on your HipMix.net profile that you have a shop, and provide the web address.
Date Updated: 04/13/2011
Log into your account
Select "My Account" on the left-hand side of the page
Enter your new information and voila! Instant username change.
Date Updated: 08/19/2011
Go to My Account and then Profile. The profile information is the same, whether you are a buyer or a seller.
Date Updated: 04/04/2011