Check the settings of the "File History drive". It still might use the old computer name or so.
https://support.microsoft.com/nl-nl/help/4026565/windows-reconnect-your-file-history-drive tells about this error message.
If this didn't happen with you in the past, maybe you didn't use the file history feature in the same way as your friend?
My computer is a desktop and is always plugged in. This is a happening on a PC I got from a friend and he said this has been happening since he changed the computer's name in one of the control panel applications, he did not mention that he renamed the hard drive as well but it looks like a unique name (doing this hasn't caused me problems in the past but I thought I'd mention it). It The message in the action center reads: "Reconnect your drive
Your file drive was disconnected for too long. Reconnect it and then tap or click to keep saving copies of your files." Once the message is clicked on a box comes up saying "Your files will be temporarily copied to your hard drive until you reconnect your File History drive and run a backup."