In contrast to Ubuntu (or even Microsoft Windows) default installations of Fedora do not send the client’s hostname to the DHCP server.

To change this behaviour, add a DHCP_HOSTNAME variable to your /etc/sysconfig/network-scripts/ifcfg-eth0 file (eth0 being your NIC’s interface name):

UUID="616426f3-ac0b-4a4a-9221-62a0055bfb07"
NM_CONTROLLED="yes"
NETBOOT="yes"
BOOTPROTO="dhcp"
DHCP_HOSTNAME="MyFedoraBox"
DEVICE="eth0"
TYPE="Ethernet"
ONBOOT=yes
NAME="DHCP"
HWADDR=00:25:22:4A:3F:F2
DEFROUTE=yes
PEERDNS=yes
PEERROUTES=yes
IPV4_FAILURE_FATAL=yes
IPV6INIT=no
USERS=user

Of course, this only works if you actually get your IP address via DHCP (since the DHCP server hands off the hostname to the DNS server). If you use a static IP configuration, nsupdate can be used to dynamically update the DNS server records. Examples and instructions on how to use nsupdate can be found at http://linux.yyz.us/nsupdate/ or http://dijks.wordpress.com/2012/07/17/register-a-hostnames-static-ip-with-your-corporate-dns-server/.