OK so you're using WMI to retrieve this information via VBScript. Here's the auto-generated VBS code from WMI Code Creator that appears to get the display name of the adapter that should match what BGInfo is pulling, based upon my simple testing.
Set adapters = objWMI.ExecQuery("SELECT * FROM Win32_NetworkAdapter",,48)
For Each objItem in adapters
Wscript.Echo "-----------------------------------"
Wscript.Echo "Win32_NetworkAdapter instance"
Wscript.Echo "-----------------------------------"
Wscript.Echo "Name: " & objItem.Name
Next
FYI, VBS is an old tech that isn't very performant and has been deprecated. I might recommend that you consider switching to Powershell which is supported on all versions of Windows, is faster and easier and has a lot more functionality. You can run PS scripts just like VBS scripts and it is effectively the replacement for the command prompt. Just something to consider.