private final BroadcastReceiver mReceiver = new BroadcastReceiver() {
    @Override
    public void onReceive(Context context, Intent intent) {
        String action = intent.getAction();

        // When discovery finds a device
        if (BluetoothDevice.ACTION_ACL_CONNECTED.equals(action)) {
            // Get the BluetoothDevice object from the Intent
            BluetoothDevice device = intent
                    .getParcelableExtra(BluetoothDevice.EXTRA_DEVICE);

                          //you can get name by device.getName()

        } else if (BluetoothAdapter.ACL_DISCONNECTED
                .equals(action)) {

        }
    }
 };

使用extendsBroadcastReceiver并在manifest中添加permissions

试试这个

public String getLocalBluetoothName(){
    if(mBluetoothAdapter == null){
        mBluetoothAdapter = BluetoothAdapter.getDefaultAdapter();
    }
    String name = mBluetoothAdapter.getName();
    if(name == null){
        System.out.println("Name is null!");
        name = mBluetoothAdapter.getAddress();
    }
    return name;
}