rename is a filesystem function and requires filesystem paths. But it seems that you’re using URI paths.
You can use $_SERVER['DOCUMENT_ROOT'] to prepend the path to the document root:
rename($_SERVER['DOCUMENT_ROOT'].'/images/old_name.jpg', $_SERVER['DOCUMENT_ROOT'].'/images/new_name.jpg');
Or for more flexibility, use dirname on the path to the current file __FILE__:
rename(dirname(__FILE__).'/images/old_name.jpg', dirname(__FILE__).'/images/new_name.jpg');
Or use relative paths. As you’re in the /script folder, .. walks one directory level up:
rename('../images/old_name.jpg', '../images/new_name.jpg');