Installing WordPress on My Web-site When I Already Have a WordPress Blog

WordPress is provided by my web hosting service as a free add-on. I have installed that add-on. However, I already have a WordPress blog. What I really want to do is to link my existing blog to my own web-site. Is there an easy way to switch the new one the installation created on my web-site for the blog that I already am running. The name of the old blog does not match the name of the web-site and I want to keep the old name, if that matters.

By the way, I am not sure how to tell which version of WordPress I’m using, so please ignore the “2.9.1” that I selected.