Thank you for your repost.
It looks like you're talking about the store configuration name: "Embedded (Default Sample Store)":
http://screencast.com/t/VtLzZ7pj123B
In this case you can rename the store configuration anytime you need:
http://screencast.com/t/jDl1viRZO8ZG
And if I misunderstood you, please provide me with the screen captures (where you can see the default database), so I could advise you on this regard.