Hi Nancy,
Thanks for reaching out about this issue you're husband's facing with caller ID when making calls from his new iPhone. We're glad to look into it with you and help in any way we can, or point you in the right direction.
To start, we can recommend ensuring that the option to "Show My Caller ID" is enabled in the Settings app on his device. This can be found under Settings > Phone > Show My Caller ID.
If enabled and the issue persists, the next step we recommend is to ensure that iPhone is fully updated to the latest version of iOS, which is iOS 13.6. The following guide has the instructions to back up his data and apply the latest update:
Update your iPhone, iPad, or iPod touch
He'll also want to check to verify that all language and region settings are configured correctly under Settings > General > Language & Region.
We're here for you if you've got any questions, or find that the behavior persists.
Have a great day!