Can I remove the SupaDupa branding from my online store?

There are possibly two parts to this question.

If you are referring to the "mysupadupa.com" that appears in the URL, then yes you may purchase your own domain name and use that as the URL for your boutique instead.

More likely, you are referring to the "E-Commerce By SupaDupa - Create Your Own Online Store" tagline at the bottom of your pages. Please see this article for information on how to do that: How to remove Supadupa Logo - de-badge credit at the footer