Hi Ayman,
Thanks for your post. Before moving on, to narrow down the issue, can I know what backup software you used? Generally speaking, when you remove a VM from inventory and add a VM from inventory in VMWare, the Virtual Center server gives it a Reference ID. When you overwrite or create a new VM, the VC gives it a new Ref ID so it is considered as a new VM. However, if you encountered the duplicate name error for the VMs, it is better to rename the existing VM with a different name in the target host and do the backup again.
Best Regards,
Ian Xue
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