I'm unclear on the distinction being drawn here:
the hostname and not mDNS
mDNS, like DNS, and hostname lists are all things a "resolver" would use to map a "hostname" to an IP address.
If you mean "how do I use DNS instead of mDNS?", you'd need to have your ESP8266 running a DNS server. And for clients to be aware of it you'd probably have to be running a DHCP server as well.
By the way, the examples list for the ESP8266 Arduino package contains a DNSServer/DNSServer example that appears to do exactly this. I have just tested it.
This is the exact code I ran out of the ESP8266 Arduino github repo at the tag for the version of the ESP8266 Arduino core I tested it on, 2.7.4.