Hey man, you are actually posting to wrong site.
This is not site for posting problems with epic games launcher or you hardware.
This site is only for Unreal Engine (game developing software)
But I try to answer your:
Every hard rive connected to your computer is named by letter (it starts from c and then goes in alphabetical order)
Every computer has drive C which is drive with windows, when you have another drive it would be named “D”.
If you connect your external drive to computer with only one drive, it will get name “D”, which is second after “C”, and if you will plug another drive it would get name “E” and then “F” and “G” and so on.
So thats why your drive changed name in other device.
If you cannot download it directly to your external drive, I would advice you to download it to your computer, and after that you can copy it to your external drive.
I dont know if this is going to help you, but I hope so