Your hostname is the name of your machine on the network (without the domain name).
Hostname is also chosen method Windows passes to the 'client-id' parameter that can be sent as an option by the client when negotiating a dhcp lease.
Most cable modem ISPs use the client-id (incorrectly referred to as hostname in Windows) as a means of identifying the machine on the subnet.
In short - your ISP gave you a client-id that they will tell you to use as the 'hostname' for your windows box; use that as the client-id in linux.
Code:
dhcpcd -h client-id-your-ISP-gave-you