To keep it short & simple:
Restore of a VM = New VM = new VM ID.
Restore VM Tags has nothing to do with your VM ID.
Ask Google about vSphere Tags
vCenter, ESX Hosts, Veeam... don't care about the VM Name. Ech VM has a unique ID which is also used for the VM selection in your job settings.
Just remove and re add the VM to your job. Don't delete the job, there is no need for it.
If you delete the Job, you have an "orphaned" backup in your repository.