Convert Woocommerce Brands name to attribute

I use Woocommerce Brand Plugin to add brand to the products. When I add a new product and select the brand name I want to appear the same brand name as an attribute as well.
I have added the below code but not sure how can I check the “product_brand” actual taxanomy name, where my brand names are stored in Woocommerce. I didn’t find any settings under Woocommerce for the plugin and also the “brand” attribute name.

I tried this code:

function transfer_brand_to_attribute( $post_id ){
    $brand = wp_get_post_terms( $post_id, 'product_brand' );
    if ( ! empty( $brand ) ) {
        // Get the first brand term
        $brand_name = $brand[0]->name;
        // Update or add the 'brand' attribute
        update_post_meta( $post_id, 'brand', $brand_name );
    }
}
add_action( 'save_post', 'transfer_brand_to_attribute' );

Any advice is appreciated.