Hello jlnmrx,
Depending on how you have this configured you may be able to use the MAC address of the VM compared to on switch(es) and determine which host this is connected to.
Other options: use RV Tools, use PowerCLI direct to hosts (connected to vCenter is not mandatory).
There *may* be something configurable in .vmx to provide such information but I can't see how much help this would be if you don't know which host it is on (and thus cannot access the .vmx) and regardless, any changes would require application and reboot of all VMs to apply.
Bob