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As documented:

Moreover we would like to remind you that restoring to a temporary URL (something like http://www.yourhost.com/~youruser) will NOT work. This has to do with the way Joomla!, Apache and PHP session management works. It has nothing to do with Akeeba Backup. Even if you install straight up Joomla! on a temporary URL you'll have problems logging in or, at the very least, with SEF URLs. This is a limitation of your server software, not something which can be addressed by Akeeba Backup and / or its restoration script.

https://www.akeeba.com/documentation/akeeba-backup-joomla/backup-now.html

The only thing you can do is attach a domain to your new host. It does not have to be the one you will be using with this site, just any spare domain you have.

You can of course assign an obviously fake domain to your hosting plan, e.g. mysite.restored  In this case you will have to assign this domain to your server's IP address using your site's hosts file (see instructions for Windows, macOS, and Linux). That's what I do when I need to transfer a site to new hosting: I use a fake domain, go through with the restoration, then assign the real domain name to the new hosting, and finally switch over the domain's DNS to point to the new server.