Joomla does not store the hostname of your site anywhere.
We read the hostname from the request when the backup is taken with any method except the CLI script for CRON jobs (/cli/akeeba-backup.php). If this is how you are taking your backups, then it's all about which hostname you access your site with when taking the backup.
When you are using the CLI script for CRON jobs (/cli/akeeba-backup.php) we cannot normally know the hostname. So, whenever you access Akeeba Backup in the administrator backend of your site (Components, Akeeba Backup) we store the current hostname in a database record which can be read by the CLI script. Therefore, you need to access Akeeba Backup while logged into your site using your preferred hostname to change that record and allow Akeeba Backup's CLI script to use it in the backup filename.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!