Hello Sanjib
When performing packet sniffing on a wireless network, there are several options. The first as you mentioned is to actually connect to the wireless network and simply use Wireshark as you would with a wired connection. Where wired connections take advantage of Winpcap libraries (for windows computers) wireshark uses what is known as Airpcap to support the capturing of wireless packets.
But you can also run wirehshark in what is known as monitor mode, which allows you to listen in to packets being transmitted by both clients and access points without actually needing to successfully connect to a network. This is one of the major security disadvantages of wireless networks, that everyone can “hear” everyone else if they are within range. Fear not however, with sufficient wireless security methods, this disadvantage is indeed mitigated. You may be able to capture all packets within range, but you won’t be able to “see” the contents of those messages if security measures have indeed been taken correctly.
In monitor mode you will be able to to capture management packets that contain the SSID even if the AP has been configured not to broadcast that information.
Keep in mind however that a lot of this is very platform/network adaptor/driver dependant, so you may get different results with different combinations of these.
In any case, you can view details of how to capture packets on wireless networks using Wireshark at this Wireshark Link.
I hope this has been helpful!
Laz