You can be able to fix this by reversing the order of the session_start() call and the statement that sets the cookie in Mage_Core_Model_Session_Abstract_Varien::start(..).
Those two lines now look like this:
$cookie->set(session_name(), $this->getSessionId()); session_start();
It now only creates one single cookie and it does not seem to have any side-effects.
The other cookie was not created in Zend_Session, instead both of them came from
This will help you to easily setup single cookie in Magento ecommerce website. Hope this article helps you in fixing your issue. If you need any other help with Magento issue fix then you can contact us or request a quote. Our technical team will help you fix all your Magento issues at an affordable price.