You can set:
$wgLDAPDomainNames = array( "mydomain" );
To any thing you want. It is shown to the user (or not shown in your case), and used for the options that proceed it, but it doesn't matter how you set it. It isn't used for authentication to the domain, and doesn't have to match your real domain name.
Ryan
I've altered $wgLDAPDomainNames in LocalSettings.php to a made up domain, but I can't login and I get the following error;
Warning: ldap_start_tls() [function.ldap-start-tls]: Unable to start TLS: Can't contact LDAP server in /wiki/extensions/LdapAuthentication.php on line 217 Log in / create account
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Again, Im probably missing something very fundamental here.
John