Hi cushtydeals -
The domain names that you purchase through Auctiva are directly related to your Auctiva Store. Everyone gets a default domain name for their Auctiva Store but the benefit of buying a personalized domain name for your Auctiva Store is that it makes it even more memorable for customers and basically gives you a website (with email addresses) so you have an even better presence on the web.
Purchasing a domain name will not affect anything except how customers get to your Auctiva Store. For you it would be beneficial if you could purchase a domain name that is close to the name of your shop that way people would have an even easier time remembering your store.
Happy Listing -