I had the same problem, I believe: udhcpc did not set the host name in the DHCP server.
When examining the problem, I learned that this is a configuration issue:
Adding the option "hostname $(hostname)" to the configuration of the respective interface in /etc/network/interfaces and reinitializing the interface (ifdown/ifup) solved the problem.
The "hostname" entry is explained in the man page for interfaces, the "$(hostname)" was just a guess (it's not explained in that man page) and worked.
However, I'd prefer this to be enabled by default as long as this can't cause other problems.
I had the same problem, I believe: udhcpc did not set the host name in the DHCP server.
When examining the problem, I learned that this is a configuration issue: interfaces and reinitializing the interface (ifdown/ifup) solved the problem.
Adding the option "hostname $(hostname)" to the configuration of the respective interface in /etc/network/
The "hostname" entry is explained in the man page for interfaces, the "$(hostname)" was just a guess (it's not explained in that man page) and worked.
However, I'd prefer this to be enabled by default as long as this can't cause other problems.