Rename case sensitive item

I am trying to rename a folder with the same name but different case. Consider this simple code:

Rename-Item -Path C:\files -NewName C:\Files

Returns the error 'Source and destination path must be different.'

Also I have tried this:

$item = 'C:\files'
Rename-Item -Path $item -NewName ($item.Name -replace 'files', 'Files')

Which does not work. Also the -force parameter does not help.

What am I missing? Thanks.