Relevance/Analyses to know VM Manager name of respective virtual host

When BFI reports “No VM Manager” status for virtual machines, there can be a number of causes. Have you looked at the troubleshooting guide found here - Troubleshooting No VM Manager data?

Every ESXi host (either directly, or via the vCenter that manages it) running a virtual machine which is participating in your BFI implementation, must be accessible by a VM Manager Tool running under your BFI deployment.

As far as I know, the VM Guest OS has no awareness of the host where it is running. The BigFix Client can only report back the Virtual ID of the VM Guest container . You need an API call to the vCenter or ESXi host to correlate the the Guest Virtual ID with the Host it resides on. This is the purpose of the VM Manager Tool.