Understand: Complications of renaming SharePoint sites
Renaming a site is often necessary, however, the renaming can be complicating for the backup system. While the renaming makes the site content accessible on a new web address, the address acts as a redirect to a new one. Meaning if the old site is still a part of the job this causes a warning about site being renamed even though it doesn't contain any actual data.
Note: The new backup of renamed site from new address will be registered in the backup as a new site.