How to set variation name in woocommerce programmatically?

Question

WordPress

This is not a big code:

$variation_id = 6837;
$product_name = 'Product 1234 ';
$product = wc_get_product( $variation_id);
$product_name = $product->get_name();
$product->set_name($product_name . 'aaa1');
$product->save();

$product->get_name() - works, returns the name. The problem is that $product->set_name() doesn't work in any way. What did I write wrong here?