Download & install the latest iOS update on your phone, go to Settings > General > Software Update. Also make sure that your car bluetooth version or firmware is updated, you may need to contact your car bluetooth manufacturer or car manufacturer about it.
Disconnect or unpair your car bluetooth from your phone (Settings > Bluetooth) & also disconnect your phone from your car bluetooth dashboard. Rename your phone by going to Settings > General > About and change the Name. Then try to pair and connect it to your car's bluetooth & test it.
If the issue persists, backup & restore your phone as new then test it again. Follow - How to back up your iPhone, iPad, and iPod touch and Restore your iPhone, iPad, or iPod to factory settings otherwise you may need to bring in your phone for service.