How does outbound calling work?

What is the caller ID that my customers see during an outbound call?

When you make outbound calls, the calls will go out from our PRI and the caller ID that the customer will see will be landline number (Exophone) that you see in your account or one of the redundant backup numbers. If the customers call back on this landline number they will still be connected to your inbound flow (Agents).
More about it here

Can you use ensure that another number that I own shows up as the caller ID?

Unfortunately No. Caller ID masking is illegal in India and we won't be able to that.

Will I own this number?

Exotel will continue to own these landline numbers which are part of Exotel's PRIs and the ownership of these numbers cannot be transfered to you. But in case there is business exigency, and you choose to move away from Exotel, we will try to ensure on a goodwill basis that the calls that land on this number are diverted to you (at a cost).

Will this number be assigned only to me?

Yes. As long as you continue to use Exotel, this Exophone number will be exclusively assigned only to you.