Populate the feed with custom values

functions.php

<?php

function lw_woocommerce_gpf_add_brand( $elements, $product_id, $variation_id = null ) {
    if ( ! is_null( $variation_id ) ) {
        $id = $variation_id;
    } else {
        $id = $product_id;
    }
    $product = wc_get_product( $id );
    $brand = $product->get_meta( 'supplier_brand_name' );
    if ( ! empty( $brand ) ) {
        $elements['brand'] = array( $brand );
    }
    return $elements;
}
add_filter( 'woocommerce_gpf_elements', 'lw_woocommerce_gpf_add_brand', 11, 3 );