If my ultimate goal is to use WP for a web site (or two) and a blog (or two) why would you not rename (through PHPAdmin), the database something identifiable as belonging to that site or blog?
I had to deal with that just this morning while figuring which of my three installation-script-named databases belongs to which site so I could delete the fourth one (from a previous-abandoned installation) I no longer needed.
I believe a plugin such as Better WP Security can rename a *new* database immediately after installation with no trouble, but I have decided to just leave mine as they are now that I know which is where.