Given that most users won't be running their own DNS / dynamic DNS, using mDNS (Multicast) is an option.
Iirc, mDNS underlies Apple's Bonjour service, and allows for broadcast of identity to the local network.
In ubuntu & fedora, the avahi project provides this functionality. I would suggest setting up so that the board's mac address is used as the default identity.
With mdns/avahi enabled (on a client machine), simple domain searches can then be used to find the local systems. An easier option is to just use the Safari browser's Bookmarks' "bonjour" collection to locate the board.
mDNS is part of Zeroconf (there's an o'Reilly book on the subject)
other information here:
I don't know if this is has been ported to the Arm branches of Ubuntu and Fedora (/other options), but figure that on the whole the porting process *shouldn't* be too challenging for those familiar with the process (I am more a consumer of packages, I'm afraid).
Anyway, that's one potential route to making the Raspberry Pi board discoverable - avahi can also announce services iirc.
- not having had hands-on experience with the board or emulation, I can't confirm that this is available or works, but it's an approach that can be taken.