The SSID broadcast can be switched off. However, this is not a particularly useful function as it does not comply with the 802.11 standard. There are WLAN clients that cannot handle this and will then no longer function on the WLAN. Moreover, this does nothing at all for security. As soon as a client communicates with the WLAN, the SSID can be easily determined with the appropriate software.

I haven't tried that, but I think that should also work.