NTLM authentication module mod_auth_ntlm_winbind for Apache2 omits domain name
Solution 1:
Ok, I've found a solution. The deal is configuration of mod_auth_ntlm_winbind's underlying mechanism, winbind. It is a part of Samba and uses it's config file. In my cases there was option "winbind use default domain" set to "yes". It allows winbind to manage users without domain part of username. After setting "winbind use default domain = no" in /etc/samba/smb.conf everything works fine.