Register a hostname and static IP

When an IP address is assigned to my board using a DHCP server, I can view my board’s website at http://hostname or http://IP address. But when I configure my board with a static IP address, http://hostname does not resolve (naturally).

Does anyone know how I can register my board’s hostname & IP address like the DHCP server does so that people on the LAN can view the website using http://hostname?

My board connects to a PC that in theory could do the registration. But still, I don’t know how to do this either.