You would like a specific e-mail address to receive invoices or billing-related e-mails.
For personal accounts, invoices can only be sent to the main e-mail address listed for the account. You can change the e-mail from your Account Settings, but this change would take effect on the entire account, not just for billing e-mails.
For Heroku Team accounts (except those using Heroku Enterprise), anyone with the role of Admin will receive billing-related e-mails. You can check who the Admins are by navigating to the Team view on Heroku Dashboard and going to the Access tab.
For Heroku Enterprise Accounts, please contact your Account Executive for questions regarding invoices.