You do not have to change anything with mojoPortal unless you fall into one of the following:
1) Have custom code using the old domain name explicitly. In other words, www.something.com is hard-coded in the custom code.
2) Your skin(s) use the old domain name explicitly.
3) You have content using the old domain name explicitly like for links or images. The editors included in mojoPortal do not use the full domain name for links and images but someone may have used the full domain name while using source view. Really, this isn't a huge issue. Most people don't go through the time to put links into their content without using the WYSIWYG editors.
4) The "AllowForcingPreferredHostName" key has been set and its corresponding setting in the Site Settings has been set to use a specific hostname.
If none of the above apply to this site, all you have to do is setup the domain's DNS to point to the server hosting the existing site.
Hope this helps,