Get this error: “The name of your computer is already in use on this network”

Try locking down the MAC address into the router to a specific IP address. MAC address is media access controller not the mac mini. The router will dhcp the same IP each time you connect.

There are three different hostnames that macOS/OS X uses:

• ComputerName
• HostName
• LocalHostName

Each of these values can be found in /Library/Preferences/SystemConfiguration/preferences.plist

ComputerName

scutil --get ComputerName

This is Apple "friendly" name for the computer and can be found in System Preferences >> Sharing >> Computer Name. According to the man page for scutil, it is described as "The user-friendly name for the system."

According to Apple, the ComputerName is The AppleTalk name and the default name used for SLP/DA¹. It's a zero-configuraiton protocol that allows you to set up a simple network without a DNS/DHCP server but allow you to reach the different resources via a host name.

HostName

scutil --get HostName

According to the scutil man page, the HostName is "the name associated with hostname(1) and gethostname(3)". This name can come from any of the following sources:

• The name provided by the DHCP or BootP server for the primary IP address
• The first name returned by a reverse DNS (address-to-name) query for the primary IP address
• The local hostname
• The name “localhost”

(In my virgin install of El Capitan, the HostName defaulted to LocalHostName)

LocalHostName

scutil --get LocalHostName

This is for Bonjour² services on the LAN. This is how, on a small LAN without DNS/DHCP, Apple computers can discover and interact with resources such as file sharing on other machines, printers, etc. This name gets set when you initially configure your Mac.

TL;DR

It is using "the first name you ever set" because during initial setup, it set the LocalHostName which it assumed would forever be. When you re-configured using the GUI, you changed the ComputerName which did not modify the LocalHostName.

If you wish to fix this in your router, simply set your LocalHostName using the command:

scutil --set LocalHostName MyNewComputerName.domain

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¹ SLP/DA Service Location Protocol/Directory Agent. The Service Location Protocol is a service discovery protocol that allows computers and other devices to find services in a local area network without prior configuration.

² Bonjour is Apple's implementation of zero-configuration networking, a group of technologies that includes service discovery, address assignment, and hostname resolution.