How to show different sub sites based on Member’s user name In word press?

There is a filter called login_redirect which you can use. The third parameter passed to this filter is the user object, so you have all kinds of possibilities to redirect. Like this:

add_filter ('login_redirect', 'wpse63660_redirect', 10, 3);

function wpse63660_redirect ($redirect_to, $request, $user) {
    //is there a user to check?
    if ( isset( $user->roles ) && is_array( $user->roles ) ) {
        //check for admins
        if ( in_array( 'administrator', $user->roles ) ) {
            // redirect them to the default place (dashboard
            return $redirect_to;
        } else {
            // set redirect page based on user name or whatever you want
            if ($user->name == 'user1') $redirect_to = www.example.com/client_one
            elseif ... and so on ...
            return $redirect_to;
        }
    } else {
        return $redirect_to;
    }
}