In Libby (formerly known as OverDrive), you are given the chance to update your email address every time you place a hold. When you click "place a hold" there is a box to enter the email address for the hold notification. The address you used before is automatically entered by default, but you may update it by typing a new one in to the box before you click "place a hold."
If you need to change an address for a hold that you have already placed, go to your holds in your downloadable account and click "Edit" next to the title that needs a new email for the notification. You will enter and confirm your new email address and click "Update."