I have created a Wifi Hotspot following the instructions given in this post.
But is there any way to stop it from broadcasting its SSID ? I have had a look in /etc/NetworkManager/system-connections/hotspot-name file but there is no setting to stop it broadcasting the SSID.
I am not interested in the fact that this does not improve security I just want to decrease the visibility of the hotspot.
SSIDs in 802.11 protocol are defined as 0-32 byte octets. It is indeed possible to "hide" your hotspot and the process is as simple as setting 0 length SSID in your beacon frames. According to the protocol, clients should not show SSIDs with "null" or "zero length" names.
Regular routers have that option in their control panels as "Don't broadcast SSID" or "Ignore broadcast SSID". By hand the same can be achieved by looking for the following in your hostapd files:
Read more about hostapd at gentoo wiki and its configuration here