The description has recently been modified to contain the statement "When new session name is supplied, session_name() modifies HTTP cookie". This is not correct as session_name() has never modified any cookie data. A change in session.name does not become effective until session_start() is called, and it is session_start() that creates the cookie if it does not already exist.
See the following bug report for details: https://bugs.php.net/bug.php?id=76413