Close, but not quite.

Top level domains are the .com's and .net's etc...
Second level domains would be the empeg in empeg.com

What you're talking about is a host name.
in loren.empeg.com, loren is the hostname, empeg is the second level domain, and .com is the top level domain. Host names don't have to be registered at all, as they are controlled on the host's dns server.

=]