Hi
Klemen,
It's been a couple of years since I played with uIP, but as far as I can remember I was never really successful with DHCP.
I configured static IP, and used mdns for hostname resolution... This way my device had a .local name on platforms with mdns support (linux/os x, don't know about windows).
However, mdns support requires multicast which isn't supported by uIP without a patch. I posted my mDNS implementation and uIP multicast patch to [uip-users] a couple of years ago. It's also available here:
http://jonasfj.dk/downloads/uip-mdns.tar.gz
Anyways, that's is just another way to do name resolution on local network, in case you are interested.