I am not sure what you mean by “the actual name”. If you need the class name, look in the source of the theme for extends WP_Widget. Other widget information is stored in the $wpdb->options table under keys starting with widget_. Once you find that you can use get_option( 'widget_name' ); to get information about active widgets, including the “instance” of the widget which you have to know in order to use the_widget.
This may or may not be a duplicate question, but the answer certainly applies: https://wordpress.stackexchange.com/a/97262/21376