That should be done on Asterisk, you can use the callerid superfecta freepbx module or any other way you like to do lookups on number to set the callerid name. If that is set in Asterisk, then FOP2 will show correctly.
I do not know if you can manipulate that kind of information as callerid is usually inbound, not outbound. Setting a callerid in asterisk affects your own (dialing) channel to be presented on the other side, or sets the callerid for inbound channels, but it wont' operate on 'dialed' numbers.
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How can I make it working for outgoing calls ? Is there a way ? I don't see any option for CID lookup source in outbound routes...