If you want close the incoming message from Magento admin, best approach is to mark the message as read. You can do this by following these 3 steps below. One than message is marked as read the pop-up will not show anymore until new message is received.
Step 1. Close the message
Step 2. Select See All messages from Dashboard
Step 3. Mark the message as read
Note: If you want to disable all notifications in your store you can do this by disabling the native “Magento_AdminNotification” extension installed on your store. Please note that this is not recommended as you will not receive any notifications at all and will miss also critical security messages from Magento platform.