Does iphone automatically cut off when the charge is complete

Yes, it not only stops charging, it tapers the charge rate from 80% up and stops at 100%. If you leave it plugged in the phone runs on power from the external source rather than the battery, so long term it will reduce the number of charge cycles of the battery, thus extending the life of the battery.

Further, if you enable Optimized Battery Charging and charge it overnight it will stop at 80%, and resume in time to reach 100% around the time you start using the phone in the morning.