You could get the desired name in your case 1 if you manually add the MAC address to the project name, I know it's not the ideal behavior but it's the fastest I could think of right now.
You will find your Bluetooth MAC address if you type:
rfkill unblock bluetooth //This will enable Bluetooth
hcitool dev //This will show the interface ID and its MAC address
I hope this helps you.
I'm thinking to write a script that take those values and than it put them in the configuration file at startup
because my project should be flashed on other boards and each board must have its own unique bluetooth identifier