Will there be a problem if Hostname not = Apache server name…

In my PHP4 book they advise going into httpd.conf and setting the
ServerName name
to the box name
echo $HOSTNAME.
So far I don't see a problem happening, but what if strange things happen and
inexperience prevents me from identifying them.
My box name is not what I set it. I think when I registered with Redhat via
rhn_register it was changed for me to something unique for their db.
Anyway, I hate to change something if it ain't broke.

Wisdom appreciated.