I've already given you the answer in my first paragraph but just in case I've confused you and for clarity.....
You give your server an FQDN of, let's say' mail.yourdomain.com and during installation you get to the step where it asks you if you want to change the domain name, answer yes and enter the domain as yourdomain.com (note, that's the domain name not the FQDN of your server).
Mail will be sent from the server as this: firstname.lastname@example.org, further domains can be added to the Zimbra server if you need/want as yourdomain2.com, yourdomain3.com etc.......
You will at this stage already have set-up your DNS A & MX records for yourdomain.com to point to your LAN IP (the A record) and the MX record has a name of mail.yourdomain.com - you will have verified this before you do the install by running the following commands:
If you don't understand what the output shows you then search the forums for further explanations or post it here. Setting up a Split DNS is remarkably simple and is nothing to fret about.
dig yourdomain.com mx
dig yourdomain.com any
host `hostname` <-- type that exact command with backticks not single quotes and do NOT put your hostname in there
If you have a webserver in your domain then you would have an A record that points to the IP of your web server, like this:
and anyone on your LAN that types yourdomain.com gets to the web server and anyone that types mail.yourdomain.com gets to the mail server. Does that answer your question?
yourdomain.com. IN A 192.168.x.x <-- your web server LAN IP