Hello bren145,
Thanks for reaching out and providing all the details here in Apple Support Communities. We want to help make sure you're able to use CarPlay as expected.
You've done a great job isolating the issue this far. Just to confirm, are you running the latest version of iOS on the iPhone? Are you trying to connect via Bluetooth or hard wired connection?
Have you enabled any restrictions in Settings > General > CarPlay?
Are there any profiles set up on the iPhone? You can check that in Settings > General.
You can also try changing the name of the iPhone to test as well. This can be done in Settings > General > About > Name.
Resetting network settings is also another good step to try. This can be done in Settings > General > Reset > Reset Network Settings. Keep in mind this will also reset your Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you’ve used before.
If possible, try a shorter Lightning to USB cable or try another cable. Make sure the cable is Apple certified: Identify counterfeit or uncertified Lightning connector accessories
The article below is another great resource.
If you need help with CarPlay
Keep us updated on the results.
Cheers!