I agree with Niels` suggestion of checking the database. An alternative could be refreshing the page, or navigating back and forth and asserting that you still see the value. That would imply that the data is stored.
But before that I would suggest talking with your development team (if that is the case here) and see if this check for storing in the ...
How do users verify the data is saved? I would make the test take the same path.
In your case placing an order might result into an item in the checkout shopping-basket. Find elements in the shopping basket and count them, get their text and validate that with an assert library (JUnit or TestNG).
WebDriver driver = new ChromeDriver();