Caller ID presentation or blocking is controlled by the calling service provider, not by your OBiTALK hardware or its configuration, in most cases. Some service providers allow their customers to send a different caller ID than the one assigned to that registered extension, and this might be controlled either by a user setting on the service provider's website, or by SIP commands.
Geoff's link to the Callcentric FAQ explains this in detail. Their mention of SIP parameters applies to non-OBi users, using a PBX or other software calling method.
When you set up Service Providers on the OBiTALK portal, it asks you if you want to use that SP as the primary line for outbound calls. If you check the box, it will route outbound calls through that SP by default. Thus, that SP's carrier will send your numeric caller ID with the call. So, for example, if you have PhonePower on SP1, Google Voice on SP2, and you set SP2 to be used as the primary for outbound calls, your outbound calls will display your GV phone number to the called party.
You can use the * commands to unblock caller ID on an individual basis. If you are using Google Voice, you can also control this in Google Voice settings (
https://voice.google.com/settings).
Callcentric doesn't support true anonymous calling. They don't want to deal with the legal issues associated with anonymous calling for deceptive purposes. Instead, you can either verify another number you control and use that number as the CID, or use your Callcentric 1-700-xxx-xxxx number (which can't be called over the PSTN), or, if you use the * code for anonymous calling, it will send the Callcentric main phone number instead of yours.
Caller ID on calls to toll-free numbers can't be blocked.
Opinion: with the explosion in robocalling, most people will not answer anonymous calls, nor should they, so using anonymous calling is not very useful now. It makes your calls look like spam.