What needs to be done to get phpSysInfo to show the correct hostname?

The problem not in phpSysInfo, you can resolve this problem thru SSH..

SSH into your server:
===1===
pico /usr/local/apache/conf/httpd.conf

use [Ctrl+w] to find "plain.rackshack.net" then replace it with "your.servername.com"

use [Ctrl+x] to save and exit
===2===
pico /etc/localdomains
find then remove "plain.rackshack.net"

use [Ctrl+x] to save and exit
===3===
pico /etc/hosts
find then remove "plain.rackshack.net"

use [Ctrl+x] to save and exit
===4===
Restar HTTP/Web Server (Apache) thru your WHM

Works like a charm, thanks!