if you are just changing the domain that is typed into the browser to access the site, than you shouldn’t have to change anything (with the exception of things like Virtuemart where having the correct url is important).
If you are actually moving the site files to a different place on the server in order to have them accessed by the new domain, then you might have to do some editing of the configuration file.
Again, if you are leaving the site files where they are, and just accessing them through a different domain name that is pointed at the same location, you shouldn’t have to do anything for Joomla! to work correctly.