Just use home.arpa from https://tools.ietf.org/html/rfc8375 with a custom DNS server or host file. Or one of the many dynamic DNS systems.
https://github.com/PowerDNS/pdns
It's also fairly complete, used in production by some pretty big ISPs.
For a light weight approach instead, Dnsmasq is good:
http://www.thekelleys.org.uk/dnsmasq/doc.html
It's what most home routers (and lots of other stuff) embed. :)
It’s just a bit of a pain to maintain if the only thing you care about is connecting to server nr 192.168.0.x
I could certainly do it, but there’s 5 services in my house I’d care to connect to, and remembering 1-5 is just as easy as giving them all names. The marginal gains are very low.
Personally I tend to throw the more stable IP addresses in /etc/hosts, as that's simple too. :)