• Avoid using their name in public places, including on the internet. Whether people are just sensitive to privacy for personal reasons, or they are celebrities, throwing their name around is offensive to them. If you write something on the web, just say "my friend" or something like that. They will appreciate it. I even know some people who use "code names" in restaurants or places like that because they prefer not to hear their name shouted out in public. If you think that this is stupid, or paranoid, well, you just don't understand. Yet.
• Never, ever post a picture of them on the internet. If you're wondering, "what harm could it do?", consider the harm a celebrity can suffer when an unauthorized image of them leaks out. If you want to treat people with respect, treat them as if they were a close personal friend who is also a celebrity.
• Don't even THINK about revealing their email address or their phone number. Ever. If someone wants to get in touch with them, get the email address or telephone number from that person and let your friend decide if they want to initiate contact. This is always best practice.
At the risk of sounding like one of those promotions against movie piracy, you wouldn't wouldn't open a bathroom door when someone requires privacy, would you? Well then keep that in mind when you think of protecting privacy in general. When in doubt, hesitate.
We all like a little privacy!