HD ships everything in a plain brown box with nothing saying "HairDirect" anywhere on it. I think the last one I got just had their return address showing. Unless someone gets really nosy and googles the address (very unlikely), I think you'll be safe.

Inside the box along with the supplies you order, you'll find an HD invoice and a few other printed marketing materials that you can just shred or throw away. Usually they send you a coupon advertising a percentage off your next order, so be sure to look for that to keep.

HD has one of the best shipping systems I've ever dealt with. From the moment you check out a tracking code is assigned to your order. You can look online to see where your package is at at any point during processing right up to the time it's delivered to your door. Also, if you order over $50 worth of products online, shipping is FREE within the continental U.S.
If you find you don't like a product for some reason, they have a 30 day/no questions asked/money-back guarantee. As long as it's returned within 30 days you can get a refund.