You already know you have access to the Azure Health Dashboard to have a look on all your Azure resource and if there is any incident or advisory.
But this is more a reactive situation than pro active.
You can now create a service alert to be notified immediately when an incident occurs.
To create a notification, just logon to your Azure Service Health Dashboard and click on the Create service health alert on top of the map
Then configure the notification you want to receive by naming it, selecting the subscription associated with, the resource group and finally the service(s), region(s) and type (NOTE I have edited the screenshot to show all the important options at once)
If you want to Edit an existing notification, just access the Health Alert blade to edit the existing notification(s); you can also create the notification from there
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