Я нашел решение моей проблемы.
SELECT wp_vendor_customer_chat.*,us.user_nicename as sender_name, u.user_nicename as reciver_name FROM wp_vendor_customer_chat
left join wp_users us on wp_vendor_customer_chat.sender_id = us.id
left join wp_users u on wp_vendor_customer_chat.receiver_id = u.id
WHERE wp_vendor_customer_chat.id IN (
SELECT MAX(id) AS last_msg_id
FROM wp_vendor_customer_chat WHERE `receiver_id` = ".$vendor_id." OR `sender_id` = ".$vendor_id."
GROUP BY IF(`sender_id` =".$vendor_id.", `receiver_id`, `sender_id`)
)
Я опубликовал решение, потому что если кто-то столкнулся с той же проблемой