The best way to handle this will be to create a new connection file with the same name as the original. Not only is the connection name referenced, but there are multi[le references to variables created in the connection file, if the connection file is created using a different name, the variable will have a different name.
If the connection is created using the same name, the only thing that may need to be adjusted is the relative path to the connection in the connection include. The connection include will look li9ke:
<?php require_once('Connections/ConnectionName.php'); ?>