My Mac mini's computer name keeps changing when it resumes from sleep

Usually this is the fault of the router and the Mac is responding to conditions out of its control.

Have you tried using a fixed IP address or making a DHCP reservation so that your Mac more reliably claims the same address when it wakes from sleep?

This has gotten much worse with iOS 8 and OS X 10.10 and there are several bugs in the new discoveryd daemon that replaces mDNSResponder for DNS naming and device discovery and routing. Basically, even computers with one network connection, there are two IP addresses - one IPv4 and the other IPv6 and the system is confusing one for the other and incrementing the host name.

I've seen this happen when the local DNS server has DNS caching enabled, but doesn't flush the cache often enough (or at all).

You can set your Host Name/Computer Name to a static value using scutil in Terminal. This means that your Mac will no longer change it's name automatically, so it's important that there are no other machines on your network that actually have that hostname. When you run this, replace "new_hostname" with your desired hostname:

sudo scutil --set HostName new_hostname

sudo scutil --set LocalHostName new_hostname

sudo scutil --set ComputerName new_hostname

You can check to make sure the values are set by running:

scutil --get HostName 

scutil --get LocalHostName 

scutil --get ComputerName 

Sources: man scutil

https://developer.apple.com/library/mac/documentation/Darwin/Reference/Manpages/man8/scutil.8.html

http://osxdaily.com/2010/09/06/change-your-mac-hostname-via-terminal/

This happens to me on occasion most typically when the OS has some sort of hiccup and needs a cold restart.

1. Unplug the router. For some reason after the restart, the computer has trouble connecting with the network as the, router "thinks" that a connection was never broken in the first place. Given a connection can't me made with the given username, the operation system adds a (1, 2, 3…) to the end of the name.

2. Restart the computer.

3. Go to preferences/Sharing and change the name of your computer from "Your Name's iMac (2)", to "Your Name's iMac"

4. Plug the router back in.

5. Connect to the network.

Worked for me!