Zimbra has serious issues with using consistent contact names.
I have rounded-up a number of closely-related bugs into one, and hope people will vote accordingly if this bug concerns them, to help get this moving as it's currently not targeted for any release.
Please vote and/or comment here: Bug 35494; Use more appropriate contact name fields - use fileAs value not fullName or sender display name in email and contact views
The basic issues is that Zimbra shows a user's contacts, and contact names in emails, using a variety of different sources.
A few examples of this bug in action:
If you view a list of emails from your contacts it shows them using the display name they chose when they sent the email - NOT the fileAs name from your addressbook - which is exceedingly frustrating when you want to scan through a batch of new emails and figure-out who actually sent them at a glance. If you're expecting an important email from Marjory Blane, but she uses her first and maiden name as her display name she'll show up as EM Blaus in mailbox, and you may well miss the email. If she decides to get funny and use 'Mickey Mouse' as her display name then you're really in trouble.
This is really a big usability oversight for Zimbra and would be (AFAIK) really easy to resolve.
When you compose an email, the autocomplete uses the fileAs value you have chosen for your contact name, yet upon selecting a contact Zimbra promptly places the 'fullName' value as the recipient. So if you have a contact with three middle names such as Jamie Ongo Lewis Parr Darryl - the fileAs value will probably be Jamie Darryl, but when you compose an email Zimbra will then enter Jamie Ongo Lewis Parr Darryl as the recipient. This is embarrassing for the user and the recipient (who may not want their middle names exposed in a group email for example).
If you view a contact in contact view it shows them using the 'fullName' field value - this is a field set when a contact is created, but which a user cannot change or view (but which is changed by other apps such as on Windows Mobile Pocket Outlook).