Thanks Igor! That works nicely
Here's the working slackware 11 specific script for posterity
-------------------------------------------------
#!/bin/sh
path2conf="/etc/apache";
newip=`ifconfig eth0 | grep "inet " | awk '{print $2}' | cut -d: -f2`
sed -e "s/ServerName[ \t+]\([0-9]\+\.\)\{1,3\}[0-9]\+/ServerName $newip/" $path2conf/httpd.conf >$path2conf/httpd.conf.new
mv $path2conf/httpd.conf $path2conf/httpd.conf.bu
mv $path2conf/httpd.conf.new $path2conf/httpd.conf
/etc/rc.d/rc.httpd restart
echo "ServerName assigned to $newip. Apache restarted.\n"
echo "Thats All Folks\n"
----------------------------------------------