Hi, Sarah. It’s exciting to hear that you’re about to launch your website! We’ve got a store launch checklist here to help you confirm that it’s all ready to go.
To confirm, are your marketing emails being sent with Shopify Email? If so, there’s a setting within the editor to determine whether or not the footer includes your shop address. Regarding the address that is pulled into the other customer notifications under Settings > Notifications, I believe this is pulling from your Default location under Settings > Locations.