By default woocommerce does not add a first name upon creation of the account.
This was my solution to getting it working if you still need it ??
add this to functions.php
add_action('woocommerce_new_customer_data','add_first_name_on_account_creation');
function add_first_name_on_account_creation($new_customer_data){
$new_customer_data['first_name'] = isset( $_POST['billing_first_name'] ) ? trim( $_POST['billing_first_name'] ) : '';
return $new_customer_data;
}
customer-new-account.php
<?php
$user_email = $user_login;
$user = get_user_by('login', $user_login);
$first_name = get_user_meta($user->ID, 'first_name', true);
?>