We tend to actually put our efforts in the 'other' direction, meaning, even if the call is signalled as anonymous, we show the CID if provided.
If what you want is to not have is showup on the phone's of your 'agents' then you should just be able to run all your calls through a 'custom' inbound context which clears out the caller ID.
Something as follows, in the trunk configuration, instead of setting the context to from-pstn or from-trunk, which are the most common configurations, you would send it to 'from-tipline'
Then you create the from-tipline context in extensions_custom.conf
[from-tipline]
exten => _NXXNXXXXXX,1,Set(CALLERID(number)=0000000000)
exten => _NXXNXXXXXX,n,Set(CALLERID(name)=TIPLINE)
exten => _NXXNXXXXXX,n,Goto(from-pstn,${EXTEN},1)The above assumes your calls are coming in with a 10 digit DID, you can adjust the dialplan as needed for the way your DIDs are comining in. I think the results are self explanatory. I can't recall, but believe that the original CID may end up somewhere in some of the CDR or CEL records even when doing this, so if you need that to be addressed, then there may be more involved and even then, your provider will probably have it. This should hide it from your agents.
