In reality, when using DHCP with a reasonably long lease time, you'll find that the client PC's IP doesn't change. If you configure the client PCs to do dynamic DNS update (which any relatively recent OS s/b capable of), and configure DNS servers to accept these updates, you can use any of the standard nslookup utilities to map the client IP to machine DNS name.
Alternatively, the IT folks could reserve IPs based on MAC address.
Thirdly, the arp cache on your server should contain MAC to IP mappings for each client that accesses your service. If the client PC IP changes, so does your local cache.