Ked si v domene tak sa overuje uzivatel na domenovom serveri, t.j. uzivatelske konta su tam.
Ked sa chces prihlasit na lokalny ucet tak tusim zadas prihlasovacie meno vo forme
nazov_lokalneho_pocitaca\lokalny_user

P.S. alebo:
http://social.technet.microsoft.com/Forums/en-US/w 7itprosecurity/thread/bee26f30-23b2-4c44-8ea1-e43f ee1fed08

If the computer is joined domain, after log on and log off a local account, the local account will still exists on logon screen.

After click Switch User, domain name will be listed below username (as you said) so we just need to input the domain user name.

Administrator is the name of the default local account. So if we input administrator, "domain" will change to computer name as Administrator is a local account.

We may not able to find other option to make switching from local/domain user account easier, but we can input ".\kids" instead of "kids-pc-01\kids" when trying to log on local account. This should help logon local account a bit easier.