You can specify who the alert notifications are sent to by supplying either Recipient Users, Recipient Groups, or both.

The buttons and can be used to add users or groups t the list of recipients for the alert notifications;

After clicking on a window titled "Add User" will open;

At the "Domain" prompt specify the domain of the user, then at the "User" prompt type in the users' name then click , and the specified user will be added to the list of recipients that the notification will be sent to;

The same process can be used with groups to send the notification to all members of the selected group (or groups).

You might want to tick "Send a carbon copy to the initiating user" if you want the user to be notified as well. 

Finally, click "Save" to save this new alert