If outbound calls are anonymous while you want to send your own CallerID, there are a couple things to check. 

1. Is the CallerID set in the PBX also added to the SIP Trunk settings on Kwebbl?

2. Is the CallerID set in the PBX in E.164 format? (eg. 31201234567)?

3. Is anonymous calling disabled in the PBX?

After these settings are checked and the issue still occurs, please raise a ticket. We would appreciate receiving answers on the questions above and also if available a log from the PBX. The logs will help us determine the issue quickly.