In order to support multiple applets in the same page, all the IDs must be different.
wordpress_processing_embed.php, you could have a counter:
global $pembed_id; ... $settings['name'] = preg_replace('/^.+\//', '', $settings['name']) . (++$pembed_id);
You may also consider stripping non-alphanumeric character from the name. You never know if that path has junk characters in it.