where/how does the virtual server hostname show up on the BIGIP

Yes I'm just using the pure windows ping. So it seems inconsequential. So does the VM just present itself by its IP? I just don't understand how the BIGIP fits into the windows network as far as name resolution goes.

At its core, a virtual server is represented by a destination IP and port (layer 4). Anything at higher levels (layer SSL, layer 7 HTTP) is managed inside the proxy. Any name resolution would be handled just like any other network device, with either DNS or Hosts entries.

so how does a VM on the BIGIP handle authentication? Is there a doc or does it use windows?

That's a very big and very complex question. There are literally innumerable ways to do authentication with BIG-IP. I'd recommend you begin by reading the quick start guide for the Access Policy Manager (APM) module.