Why can't I have more than 1 database's

I currently have two site’s (full) and have created several Databases with no problems, but no matter wich one I logg in to they all show the same tables, should they not be seperate form each other? on my other host when I have Multiple site’s they each have their own data base,and you can’t see the others Table’s, when I make a Db dump it’s for that site only.
Is this possible here?

I think you’re running into the same problem that I was. If you truly want your databases to be separate, then each databases’ username must also be different.