If your Apache ran on Windows, you'd be able to get the info from $ENV{REMOTE_USER} with the following configuration bits:

LoadModule sspi_auth_module modules/mod_auth_sspi.so

<Location /here>
    AuthName "Some realm"
    AuthType SSPI
    SSPIAuth On
    SSPIAuthoritative On

    require valid-user
</LOCATION>
[download]

Unfortunately, I have no idea if that would ever work on a Unix server (and I doubt it), but I thought I'd throw it out here anyway. It might just give you a lead to google on.