You would need to create a static DNS entry on your DNS server for the ESXi host. It's not going to automatically create a DNS registration for you.
Edit:
It is possible to have an ESXi host perform a dynamic DNS registration (DDNS) if you go into the bowels of the ESXi command line and instruct it to...
It's a strange request, as adding a static entry is usually the path of least resistance, but try the following:
esxcli system settings advanced set -o /Misc/PreferredHostName -s host.domainname.com