The most network-agnostic way to specify a hostname for a host on the network is through DNS, which your device itself cannot control, but all is not lost.
In most environments, the DHCP and DNS servers are tied (AD in Windows networks, DNSMasq on linux, etc...) so your best option is to rely on this behaviour. When you request an IP using DHCP, the DHCP protocol allows you to specify the hostname you'd like to use and if the network is set up to allow DNS entries to be created and maintained by the DNS server, the hostname you send during your DHCP request will typically be used.
The DHCP parameter is called 'Hostname'. The Network protocol documentation for this parameter is located in RFC 2132, and explained here.
Unfortunately since i just joined the site, I'm not allowed to post more than one link, so I can't link the RFC but you can just google for RFC 2132. Good luck!