To expand on the previous, ITSPs that allow arbitrary caller ID to be forwarded have given VoIP a bad name, e.g., in the UK, it is common for phishers to present the published, incoming number, of a bank, and it is very common for them to present random numbers, or ones similar to that of the victim (to prevent blocking, and to make them think it might be someone they know).
Please explain what you have changed. From POTS? PRI? Different provider/carrier?
Which country? In the US, if the provider/carrier supports it (e.g. Bandwidth via AnveoDirect, though there are many others), you can send a caller ID that is not yours and the carrier will sign it with “B” attestation (they know the customer but not the number). At the receiving end, with default settings, the mobile carrier will withhold the “Verified” indication, but will not block or otherwise interfere with the call.
I am assuming that you are forwarding to staff mobiles. They need to be instructed to not choose the option (with their mobile carrier) to block B calls or send them to voicemail.
Another thought: I doubt that your issue is STIR/SHAKEN related, which typically causes calls to be labeled as spam/scam, or blocked outright. I suspect that either your outbound caller ID is not formatted or in the proper header as the provider expects. Did they provide documentation on how to send caller ID?