Welcome to the forum.
There is a thread in this forum where users modified their Nano 33 IoT to support Bluetooth Classic.
https://forum.arduino.cc/t/can-the-nano-iot-33-run-full-bluetooth-not-ble/626990
Use at your own risk. 
I have not tried this myself. There is no support by the ArduinoBLE library.
As for phone changing address and some device not showing the name. That is intentional. Smartphones are used by almost everyone nowadays and most have no idea what they are doing. So, phone manufacturers have decided to make tracking phones via BLE impossible by randomizing addresses and not advertising any identifiable data. The exact process is not standardized and can be changed at any time by the phone manufacturer when new ways of tracking would be discovered.