How to set up my ESXi host in DNS

My ESXi 6.0 host can be seen by IP address but not by hostname.

i.e. "ping 192.168.1.12" works, but "ping ESXi6" fails.

Is the solution to add a New Host record in DNS?  Assuming yes, I did that.

Now, "ping ESXi6" still doesn't work, but "ping ESXi6.Mittens.local" succeeds.

But how does that work?  The host boots first, and then the DC boots as a VM on top of that host.  How can the host be part of a domain that doesn't exist until after its VM boots?  

In particular, in my vSphere Client:  host --> Configuration --> Software --> DNS and Routing --> Properties, should I enter the domain name there?

Thanks