I'm sorry to hear you are having this problem with your call identity.
I would start by suggesting to clear the pairing list on your headphones. You can do this by holding the Bluetooth switch for approximately 10 seconds until you hear the prompt "Bluetooth device list cleared". Then you should remove the headphones from your device list on your phone.
I would also recommend that you check for the latest firmware updates. You can do this by using the Bose Connect App where you will be prompted to update your headphones or visit btu.bose.com on your computer and follow the instructions on-screen.
Let me know if you are still having this problem after trying the above steps.