Find Ethernet MAC Address on MacBook 12″

This depends a lot on your DHCP server, but I would look into using the client id to assign static IPs. It's not tied to the individual hardware (although you'd have to set it at least once when they first use a TB Display), so it avoids the switching displays problem. It can be set via the networksetup tool.

The MAC Address is unique and a property of the actual network hardware (although it can be spoofed). So your adapter has its own MAC address, as does the the network interface in a Thunderbolt display, and the Wi-Fi in your MacBook Air.

Different Thunderbolt to Ethernet adapters will have different MAC addresses, but moving one between different ports won't change it.

You can view the MAC address of any network interface attached to your Mac by using Network Utility, which you'll find in the Utilities folder within your Applications folder. It calls it a Hardware Address, but it's the same thing.