There's no real need to memorise IP addresses, that's what DNS was made for. If your servers are on the internet at large then they probably have DNS already, and if its a local network then most operating systems will now automatically work out where machines on the .local domain are (I'll be honest, I don't fully understand how that works).
I've had only a very limited exposure to IPv6, but it seemed to me that the slogan "DNS solves it for you!" doesn't really pan out. It solves it if you're on a well-set-up network and have your DNS up and running happily, but with the ad-hoc networks my [limited] experience has seen, it hasn't been trivial. Essentially, it means you have to run an interpreter service (the DNS) to understand the network - one more bit of software to configure and troubleshoot... though to be fair, IPv4 was also quite confusing when I first started playing with it.
The word you probably wanted to use was “Zeroconf”.
“Zeroconf”¹ is a name for the sum of two interacting standards, namely mDNS”² and “DNS-SD”³. Avahi⁴ is a free software implementation (for Linux and BSD) for a service where programs can register Zeroconf services (name & port number) and have Avahi announce them on the network. The other major implementation of a daemon of this kind is from Apple, and it is called “Bonjour”⁵.
This often gets confused, so, again: Zeroconf = standard. mDNS and DNS-SD = component standards. Avahi = A specific free software implementation. Bonjour = A specific proprietary implementation.
