Even if you turn off broadcasting of
SSID in the AP (which you should do),
SSID is still sent in clear text when clients associate to an AP... When
SSID broadcast is off, the sniffer would have to wait for a valid user to associate to the network in order to see the
SSID.
In other words, not broadcasting the
SSID would delay, rather than prevent a sniffer from obtaining it. Still, turning off broadcast pings on the Access Point makes it invisible to
802.11b analysis tools like NetStumbler.