Internal queues - redact caller ID?

[Vik]

I have some internal queues for one department to call another.
The receiving department staff are cherry picking calls and ignoring some incoming calls to the queue if it's Person A or Person B, but answering if it's Person C or Person D.

Is there a way I can hide the caller ID to the internal queue, while leaving the caller ID visible for all other internal calls (direct, other call groups, queues)?
I.e. Receiving department just sees 'Call' and doesn't see who the specific internal caller is?

I've looked through all the queue settings, but cannot see an option that gives me this?

 

[Vik]

So far, the only solution is to make the name of the queue so long that it's too long for the softphone display so that the receiving department can't see the name unless they hover their mouse over it.
It's the low-tech solution

I'm sure there must be a full-tech solution I'm just not seeing?