By default, Hudson uses ADSI to talk to Active Directory, and doing this doesn't require the domain name to be configured.
However, while unconfirmed, there are reports that this mechanism fails if the user account that's running Hudson is not a domain user (which is the case if you install Hudson as a service, for example.) In such a case, please specify the domain name explicitly here, and Hudson uses standard LDAP protocol to talk to Active Directory.