There are some issues have been reported to Apple about show my caller ID setting grayed out and can’t be changed even though their carrier has been enabled it for them. This appeared to be a software issue on iPhone and can be resolved by following the simple steps below.
First thing that you need to make sure is thought that your carrier has already been enabled it for you, they’ll do that for free of charge for most of the countries worldwide. Make sure it is enabled.
Then you can try to tun on Airplane mode and turn back on, then try to change the show my caller ID settings.
Still no luck?
Then turn on Airplane mode then go back to the show my caller ID settings and you’ll be able to change that settings now.