Blizzard has added an opt-out option to the Real ID system being implemented with World of Warcraft and StarCraft II and likely Diablo III.
According to an official post over on the World of Warcraft forums, Real ID can be disabled, and only the character level of friends and players will be listed.
There will also be two options for users of the Real ID system, which is explained below:
We’d like to make you aware of the new Real ID-related privacy options we’ve introduced to Battle.net. These options provide Real ID users with additional tools for customizing the service based on their preferences, enabling the ability to opt in or out of the Real ID “Friends of Friends” and “Add Facebook Friends” features or to turn off Real ID altogether.
Real ID offers an optional, convenient way for keeping in touch with real-world friends you know and trust, whether they’re playing World of Warcraft, StarCraft II, or one of our future games. The “Friends of Friends” and “Add Facebook Friends” features provide you with even more options to stay connected while you play by making it easier for real-life friends to locate each other on Battle.net.
Users who wish to change privacy setting in their account can do so through the communications preference section of Battle.net.