I've never heard of anything like that ever hapenning before. Are you able to consistently re-create the problem? And thus collect before and after evidence, before you start trawling through logs.
Never seen this but there is possibility.
If you are backing up by "hostname" NBU gets the vm-machine IP address and does a reverse DNS lookup and saves it under the hostname that DNS provides. If there is no DNS resolution of the IP address it will save the machine as an IP address i.e. no hostname. But if there are two machines with the same IP address my guess you have a problem, it all depends what DNS returns to NBU. I would do a DNS lookup and flush the DNS cache on the NBU servers that interact with the vmware. What you see on the CLI may be different what is cached.
If you do suspect two machines with the same IP address might be an idea to to check with those the assign IP in your company or own the process if its a self-help service.
I could see in the logs that the name of the machine on the OS is different than could be seen from the vmware. At the end of the backup job this change the name that came out vmware by the name it had on the OS.
The Display Name (aka Virtual Machine Name) attribute is something that can be changed anytime has nothing to do with OS or DNS. Display Name is strictly internal to VMware and used in identifying the guest machines for administrative purposes. When a Display Name is changed by the VMadmin it has no affect on the internals of the guest machine as it's a vmware tag for human consumption. Commonly used when you want to do a restore and keep the old machine.
I tend avoid the use of Display Name backups because you don't have knowledge what the VMadmins are doing. This type of backup does have its uses usually where DNS resolution isn't available.
VMadmins use the term (Virtual) Machine Name, they haven't a clue what a Display Name is - its only used by NBU people.