View incoming caller ID to extension 1 on extension 2's display

Call comes into extension 1. Should not ring extension 2. However, extension 2 needs to see the incoming caller ID so, if necessary, extension 2 can pick it up (using the feature code for Call Pickup).

Sorry I don’t know if there is a name for this, otherwise I would be able to search for it.

System is Asterisk 11.19.0 with Yealink 23G phones.

I think you are out of luck with those phones. Sangoma has the feature (called BLF Alerts). When enabled you get a visual (or audio) notify when one of your BLF extensions are ringing.
http://wiki.freepbx.org/display/PHON/BLF+Alerts

I already have the BLF working on the 23G so I can see when the extension is in use (turns red) or ringing (flashing red). But what I am looking for is to display the incoming caller ID.

Knowing that another phone is ringing via BLF is usually pretty straight-forward, but getting the Caller ID information on that call is a LOT more interesting.

Essentially, you’d have to set up a custom-context for phone 1 that populates a hint and then display that hint’s value on the screen of phone 2. If you do manage to get it working, please post your code so we can see it.