Who is your trunking provider? They may have toughened their CID requirements to make it harder on scammers.
Try this test: Temporarily change the Outbound CID for your desk phone extension to one of the numbers you want to use for Fixed CID. For example
"John Doe" <12125551212>
Call your mobile and see whether it is correctly displayed. If not, your trunking provider or mobile carrier is likely rejecting the call.
Be sure that you are using the correct format. Some providers expect 2125551212, some 12125551212 and some +12125551212. The format that they send you on incoming calls will likely be accepted for outgoing.
Some providers won’t allow you to send an arbitrary called ID – it must be a number that they know is yours, either because you bought it from them or verified it on their portal.