manual Cox cable config

I made the conversion this morning and while almost everything "seems to
be" working I was wondering if anyone could answer a couple of
questions.

It seems that the old host names will continue to work i.e. CXxxxxxx-x.
Is that correct. Or can they now also be changed?

How about domain names? My old name would have been
CXxxxxxx-x@chdn1.az.home.com. What is the new domain name?

Is the resolve.conf file to be "deleted".    I assume we are no longer
to specify nameservers.