Most "celebrities" probably don't even want to be called "celebrities", so let's just call them people who are in movies, for the purposes of this blog post.
I started this topic in the Forum to gather thoughts on the subject, called "What to do when a celebrity buys your product". But then I realized that there really is only one thing to: ship them the product and go about your busy day. A "friend" of mine (because I would never do something this thoughtless, of course) had an order from a person who is in movies. She knew this because the famous person just put down their name in the shipping area, just like any person would do. It was the person in the movie's attempt at being normal, and not having to set an alter ego in order to perform a normal and enjoyable function of life: online shopping.
So, if this happens to you, just know, that even if your friends are doing it, and leaking to everyone that so-and-so bought this, take your hands away from the keyboard, get a glass of water (not coffee, because who knows what you're capable of at that point), and think. If you feel that this person's testimony would help your brand, then treat them as you would any other person who is not sought after by cameras, and politely ask them, or let them know how to go about submitting a review, if you have such a function on your website. Otherwise, they are just a normal person, a wonderful customer who enjoys your product.
Sure, there are creative ways you could work together if they think they can help your brand, but approach these ways with care and respect. Otherwise, you may be served with an email from a disappointed customer, and a lawyer letter, warning you of your actions.