When I have needs for different connection files I will usually keep them named the same if possible and just update the details of the local or live file to point to the proper db. This way you can have completely separate connections for local and live, but if they have the same name there is no need to update the code that makes use of the connection.
You can update the connection used within the Server Behavior interface or by doing a manual find and replace in the site for the old connection values and updating them to the new one.
