When sending a package, you have the option to receive a notification when your package is opened. However, there's no official "sent notification" confirmation.
To receive a notification when the package is sent, just include yourself as a recipient on your own package.
Make sure the "Send e-mails" share setting is toggled ON. It is by default on most packages.
Once sent, you will get an e-mail alert that a package is shared with you. You will also see the package in both your CORE package inbox and sent box.