From all my testing that I've done on SSID and wireless, the SSID cannot be encrytped. And as everyone as all ready stated, you can stop the broadcast. But there are quite a number of tools that can eventually pick up the beacon packet and divulge the SSID.

Kismet is one of the tools. This little intrusion detection device also couples as hotspot detector. It can even associate IP and MAC addresses from machines to the networks it hears. Since it runs in monitor mode anyways, it can pick up plenty of wireless networks across the spectrum. And makes some cool noises when it picks up on certain type of traffic

Airsnort is another good tool for checking what kind of traffic is out there. Even if you were able to manage to encrypt the SSID, this would eventually be able to decipher it (depending on the type of algorith one uses). Airsnort can crack wep 64 & 128, and maybe wpa but don't quote me on that. I know it only takes 364 some-odd thousand packets to break the 64 bit wep key. 128 is closer to a million. A good sized network could generate that kind of easy, or just start downloading fedora core 5 about 10 times simultaneously and that will generate the necessary traffic if you're interested in testing out Airsnort.

Well, that's my two cents. In short, even if you did encrypt it there are ways of finding it out