There are a few ways to hide your steam name. The most common way is to set your profile to private. This will prevent anyone from seeing your real name, but it will also prevent you from appearing in public game lists and from using the Steam Community features.
If you want to take things a step further, you can use a VPN or proxy server to change your IP address and make it appear as though you're accessing Steam from a different location. This will make it more difficult for people to track down your real identity, but it will also make it more difficult for you to use the Steam Community features and play online games.
Finally, if you really want to keep your identity completely hidden, you can create a new account with a fake name and email address. This is obviously the most extreme measure, but it will guarantee that no one can ever find out who you really are.