custom post type metaboxes not saving

You need to replace the field name from name to something else since name is a reserved word and could be whats causing the blank page, also its better practice to prefix you field names.

Now in your save_details_booktime function make sure you are no the right post type and not in autosave, something like this:

 function save_details_booktime($post_id ) {
    global $post;   
    //skip auto save
    if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) {
        return $post_id;
    }
    /check for you post type only
    if( $post->post_type != "booktime" ) {
        return;

    }
    $custom_meta_fields = array( 'name' ); //change from name to something else

    foreach( $custom_meta_fields as $custom_meta_field ){
        if(isset($_POST[$custom_meta_field]) && $_POST[$custom_meta_field] != ""){
            update_post_meta($post_id, $custom_meta_field, $_POST[$custom_meta_field]);
        }
    }
}