send unique 'clientID' to router from uno/ethernetshield

Does anybody know how an ethernet device sends its Client ID string to a router when getting its IP from the router?

I have several arduino's connected to my router doing a varity of things which I can control/gather information from via custom webpages on my computer. However when I look at my routers client id table through its web page the only information I have for each of the arduino is its MAC and IP address. Other things on my network like my Sony Bravia TV and HP printers and even this windows computer have automatically populated the table with identifying text strings as well as the MAC/IP. I would like the arduino's to do the same so that when things are moved around or new ones added or the whole system is rebooted I don't have to scrabble around finding what IP address has been given out by the router to a particular arduino. Simple strings like 'Cold Room Data', 'Generator Status' etc is all I need.

If anybody can point me to where and how I can use or I might need to modify the Ethernet library to achieve this I can make a start on resolving this issue. Or is it a question of sending an HTTP 'PUT' command to the router as you do with pachtube?