The client system does not require a particular host name.
If you want a client to request a specific host name, see DHCPv4 Client Host Names.
Default requests for the client are given in /etc/default/dhcpagent, and includes DNS Server, DNS domain, and broadcast address.
The DHCP client's parameter file can be set up to request more options in the PARAM_REQUEST_LIST keyword in the /etc/default/dhcpagent file. The DHCP server can be configured to provide options that were not specifically requested. See About DHCP Macros and Working With DHCP Macros (Task Map) for information about using DHCP server macros to send information to clients.