I have a Linux 9 and RHEL 4.

They have been doing this for a some time and working fine.

Some day, my IT guys decided to upgrade their firewall and cause ONLY my RedHat 9 to be unable to send the email to me. Not really sure what happened. I called them up and they told me to check my connection with our SMTP server and gave me it's ip addr.

But for my redhat, for their /etc/sysconfig/network are:
e.g.

Linux 9 is having:
RHEL 4 is having:
Should I change the RedHat 9's hostname to hostname=linux3-AKFMVO1S?
Or something else caused this to happen.

You have a redhat 9 client that is connecting to a network file server? Is the mail handled by the server? If so, I would think you could log into the mail server and add a .forward file to the directory you log into that is simply the address you want your mail forwarded to, so

myemail@somewhere.com

If you are using something like gmail to get your mail, and popping it from the mail server, you can go into gmail, click on settings, then go to forwarding/pop IMAP and enter the correct settings to pop mail from the server. The IT guys should know these settings. It should be similar for other internet mail sites.

It sounds like your RH system was configured to deliver
email directly to hosts on the Internet, then your firewall
guy prevented this, saying it should deliver email to the
common SMTP server, which will then deliver it to the hosts.

In sendmail terminology, you need to have a "smarthost".
I'm sure that the Red Hat documentation will be able to
guide you through this.