Rename database? Is it possible to do this without breaking the blog?

I am encountering issues with integrating wp with my existing site. It’s with the database connections. Only one of them wants to work in the page. The problem is that my existing site and wp blog are on two different databases. It will be less work if I just keep my current template/script with all of the code and just change a few things like the variables for the posts. To do this, I will need to move my posts and everything else in the 10 wp tables to a different database. I know how to export the actual database, so please let me know how I would let my wp know that the db name has changed?

edit: do i just manually change the db name in the config file? if so, is that all that i do?