Simple Filter between multiple taxonomys

Question

I create 2 dropdowns one for each category & tag and filtering posts successfully.

After that i create a custom taxonomy cat and try to filter post between all three dropdowns. But dropdown for taxonomy cat not working.

<form action="<?php bloginfo('url'); ?>" method="get">                  
<?php
// I use custom taxonomy  "Cat"
    if( $terms = get_terms( 'cat', 'orderby=name' ) ) :
        echo '<select name="cat_name"> <option value="">Cat</option>';
        foreach ( $terms as $term ) :
            echo '<option value="' . $term->name . '">' . $term->name . '</option>';
        endforeach;
        echo '</select>';
    endif;
// I use default  "Categories"
    if( $terms = get_terms( 'category', 'orderby=name' ) ) : 
        echo '<select name="category_name"> <option value="">Categories</option>';
        foreach ( $terms as $term ) :
            echo '<option value="' . $term->name . '">' . $term->name . '</option>';
        endforeach;
        echo '</select>';
    endif;
// I use default  "Tag"
    if( $terms = get_terms( 'post_tag', 'orderby=name' ) ) :
        echo '<select name="tag"><option value="">Tags</option>';
        foreach ( $terms as $term ) :
            echo '<option value="' . $term->name . '">' . $term->name . '</option>';
        endforeach;
        echo '</select>';
    endif;
?>
<input type="submit" name="submit" value="filter" />
</form>

Its not work for taxonomy cat & but working for others two category & tag

What I missing or any suggestions to make all three dropdown working?

Optional: This is how i create Custom Taxonomy cat

function custom_taxonomies() {
    $labels = array(
        'name' => 'Cat',
        'singular_name' => 'Cat',
        'menu_name' => 'Cat'
    );
    $args = array(
        'hierarchical' => true,
        'labels' => $labels,
        'show_ui' => true,
        'show_admin_column' => true,
        'query_var' => true,
        'rewrite' => array( 'slug' => 'cat' )
    );
    register_taxonomy('cat', array('post'), $args); 
}
add_action( 'init' , 'custom_taxonomies' );

Answer 1

I am answering my own question. So that others can also use these type of filter.

Replacing query_var => true to query_var => cat_name

or

any other names and use it inside Form for custom taxonomy.

Then custom taxonomy react like default wordpress category and tag.