Do you want to modify the web engine, ie the LUA/HTML code?
In this case just duplicate the gallery with the correct name coding in the manifest... see links at the end of
http://blogs.adobe.com/lightroomjournal/2009/04/web_gallery_agogo.htmlIf you just want to save another aspect of the same gallery in a new template, click on the + sign at the right of the Template browser (left panel).