Enable sip set debug and find out exactly what caller ID is being sent. If it is wrong, please provide sip.conf (with passwords removed). a verbose level three or higher trace of the call, and the contents of the INVITE sent by Asterisk (with authentication data removed). If it is right, the problem lies in the Alcatel.
I need the SIP trace (to see what caller ID is actually being sent and to see what the originating device is sending), the dialplan trace (to see if the dialplan is is setting it) and the device entry for the originating device (in case that is setting it).
It also looks like you have only provided the general section of sip.conf, so I need the device entry for the trunk.