Not able to change SSID

Hi all,

I am doing a cooperation project and I will implement two rachel-pi in the same room trying to not overload the connection and I will balance the traffic between the two rachel-pi.

For this reason I need to change the SSID, at least, for one of the raspberris. If not the computers will read the two wireless connections and they just would be able to connect to one of the raspberris.

I have tried:
ifconfig wlan0 down
iwconfig wlan0 essid "RPI1"
ifconfig wlan0 up

When I apply the change in the SSID and looking in the iwconfig I obtain this:

IEEE 802.11abgn  ESSID:"RPI1"  
      Mode:Managed  Access Point: Not-Associated   Tx-Power=15 dBm   
      Retry short limit:7   RTS thr:off   Fragment thr:off
      Encryption key:off
      Power Management:on

But when I up the server the SSID changes as the original one.
    IEEE 802.11abgn  ESSID:"RPI"  
          Mode:Managed  Frequency:2.427 GHz  Access Point: B8:27:EB:BA:4B:7C   
          Bit Rate=65 Mb/s   Tx-Power=15 dBm   
      Retry short limit:7   RTS thr:off   Fragment thr:off
      Encryption key:off
      Power Management:on
      Link Quality=70/70  Signal level=-20 dBm  
      Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0
      Tx excessive retries:0  Invalid misc:34   Missed beacon:0

Is this the expected behaviour? Can I change the ssid in a different way?

Many thanks