The HDD has the same name and gets the same drive letter but the Backup fails with: "Backup repository is not accessible".
Since it’s other device you need to manually change the target of your backup job in Configure backup wizard. Also, it means the disk recognition of the USB drive is working properly as it does not relay on the volume letter or label.
Will the feature be added in the future or is it just not possible?
If you mean support of the rotated USB drives – yes, meanwhile please change the target manually.