It looks like when you use zmprov to modify the 'displayName' attribute, it also tries to change the 'cn' attribute in LDAP as well. So, while you simply want to remove the displayName attribute, using zmprov won't work, since it's also trying to remove the cn and as the error reports, that would be an object class violation.
Using the 'ldapmodify' command line may help, if you're confident enough in feeding in the right information, and know the right credentials to authenticate to your ldap configuration.
An ldif along the lines of:
should do the trick.
That said, I'd probably want confirmation from a Zimbra employee before you proceed.