There are many ways to identify a computer, starting with MAC address. Every network interface card (ethernet adapter, wireless adapter, etc) comes with a MAC address. Your computer keeps a table of these MAC addresses and relates them to IP addresses. Open up a command prompt and run:
That will print a list of IP addresses and their matching MAC addresses. If your computer doesn't know an IP addresses' MAC address, it will send an ARP request across the entire network asking for that IP to respond with its MAC address.
DNS matches a name to these IP addresses by asking a DNS server for the A record of a particular name. This returns the IP address the computer needs. Try running:
You'll first see the name and IP address of your DNS server. Your router receives the DNS server's IP address through DHCP provided by your Internet service provider. Your computer receives the DNS server's address from your router's DHCP service. You'll then see the IP addresses related to that name. Unless you run your own DNS server, you won't be able to query your computers by DNS name.
NBT (NetBIOS over TCP) is what your computer uses to look up an address by 'Computer Name'. It's a little more difficult to explain in a nutshell, try looking it up.
Changing a single variable, such as a MAC address, might not update and propagate through the network like you would think. Lets say computername.domain.com has an A record of 192.168.1.100 and your computer has a record in its ARP table that associates the MAC address 00:11:22:33:44:55 with 192.168.1.100. Changing the MAC address doesn't change the A record on the DNS server, and won't change even change the ARP tables of other computers immediately. This may be why it seems that the computers aren't ever 'identical', yet nothing is functional.