You can join both and upgrade based on the condition.
UPDATE messages a
INNER JOIN
(
SELECT name , MAX(ReceiveTime) max_time
FROM messages
GROUP BY name
) b ON a.name = b.name AND
a.ReceiveTime = b.max_time
SET a.is_unread = 1
No condition WHERE. It will update the column is_unreadfor the last record.
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