Change WooCommerce username to emailaddress, see http://stackoverflow.com/questions/24911432/wrong-username-and-displayname-after-user-registraton-woocommerce.

gistfile1.txt

// Change WooCommerce username to emailaddress, see https://gist.github.com/Willem-Siebe/9dfe4aaaaa24e1294da6.

add_filter('woocommerce_new_customer_data','wsis_change_wc_username');

function wsis_change_wc_username($user_data) {
	return array(
		'user_login' => $user_data['user_email'],
        'user_pass'  => $user_data['user_pass'],
        'user_email' => $user_data['user_email'],
        'role'       => 'customer');
}