I have a Bluetooth speaker and a Bluetooth headphone When I connected to my iPhone the speaker is identified as a speaker and when I connected the headphone it identified it as a headphone.

1.What signal does the device send through Bluetooth to helps it identify itself? How does it do it?

2.Can I configure my HC-05(OR any chip) to act as a Bluetooth device I wish? How to do it?

 

I have a Bluetooth speaker and a Bluetooth headphone When I connected to my iPhone the speaker is identified as a speaker and when I connected the headphone it identified it as a headphone.

1.What signal does the device send through Bluetooth to helps it identify itself? How does it do it?

2.Can I configure my HC-05(OR any chip) to act as a Bluetooth device I wish? How to do it?

I'm no expert but I know where they live:
https://www.bluetooth.com/specifications

I speculate that the self-identification is just a piece of data that doesn't really do anything except communicate to the user the major functions of the device.