Arduino Nano - Unknown USB device
I found the issue!
There is a bug in the Arduino hardware:
https://ketturi.kapsi.fi/2014/04/how-to-fix-moody-arduino-nano/

You need to bridge pins 25 and 26 of the FTDI chip (located at the back of the Arduino) to ground the pin 26 TEST signal.
If I connect these pins then it works just fine!