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If you need to be enterprise class, clear out your new cloned containers log files which will reference the original container hostname. Here is an example search on a relatively new container,
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DNS Resolution - http://seminar.io/2014/07/27/dns-resolution-for-lxc-in-ubuntu-trusty/
Running X Windows in LXC - http://unix.stackexchange.com/questions/18003/linux-lxc-deploying-images-with-tiniest-possible-x11