Windows Authentication on different domain

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ASP.NET

Hello,
Sorry if this is a simple question, but i am suffering a lot. Any idea will help me. Thanks in advance.

I deployed asp.net application with "Windows" authentication on win server 2008.

Now i can access this application from network computer, but Windows Logon window comes for server 2008. (I dont want this).

Now second problem, its most important....

I used "User.Identity.Name" to get end user's login name.

When i access this application from other machine, it shows win server 2008 machine's login username.

I am unable to get end user's name anymore.
I researched, and i am thinking that, Domain of win server 2008, where asp.net app is installed, is different from where i am trying to access. I am not sure that it is causing problem or not.

Please help,
Thanks,
Yogesh