The command that controls the "Broadcast" of the SSID is "guest mode". Have a look;
guest-mode (SSID configuration mode)
Use the guest-mode SSID configuration mode command to configure the radio interface (for the specified SSID) to support guest mode. Use the no form of the command to disable the guest mode.
The access point can have one guest-mode SSID or none at all. The guest-mode SSID is used in beacon frames and response frames to probe requests that specify the empty or wildcard SSID. If no guest-mode SSID exists, the beacon contains no SSID and probe requests with the wildcard SSID are ignored. Disabling the guest mode makes the networks slightly more secure. Enabling the guest mode helps clients that passively scan (do not transmit) associate with the access point. It also allows clients configured without a SSID to associate.
This example shows how to set the wireless LAN for the specified SSID into guest mode:
This example shows how to reset the guest-mode parameter to default values (no broadcast SSID):