Welcome to the forums,
su - zimbra
zmprov gacf | grep zimbraDefaultDomainName
This is the domain allowed to login without typing the full email@example.com
You can make it easier for users by creating a virtual host so web-client users can log in without having to specify the domain name as part of their user name.
Admin console GUI > Domains > Virtual Hosts tab. The virtual host requires a valid DNS configuration with an A record.
Users enter the virtual host name as the URL address (mail.domainB.com) where they enter just their username/pass.
zmprov md domainB.com zimbraVirtualHostname mail.domainB.com
The authentication request searches for a domain with that virtual host name and authentication is completed against that domain.
Users can still visit any of your server url's and type in their full firstname.lastname@example.org/pass to login - so using the new new virtual host url is not mandatory.
If your still intent on a dialog box to select domains you might start with looking at /opt/zimbra/mailboxd/webapps/zimbra/public/login.jsp (make a backup of it first) or create your own portal to login Preauth - Zimbra :: Wiki
http://www.zimbra.com/forums/announc...html#post62754 so we know which version you're running & therefore what options to give.