Calibre server through computer name

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http://askubuntu.com – I use Calibre to manage my ebooks. Caibre has a server option, which I can access on my Ubuntu 12.10 machine through the link: http://my_computer_name:8080 or through http://my_IP_address:8080. On another machine on the local network, I can access the server through the IP address but not through the computer name. Since the IP address changes every time I connect, I wish to be able to connect through the computer name. How do I go about it? Some information: There's a router which manages my network but I do not have much information on it, since I'm not administrator of the network. Ho (HowTos)