All recent document should NOT show on the home screen for everyone to see.
Why do you allow others to work under your login? The thumbnails you see on the start screen belong to the recent document list. And this list is stored in your private account folder. If another user uses your PC with his own account, he will not see this list.
You can empty the recent file list in menu File > Recents Documents > Clear List (=last item). This erases the thumbnails too.
If it is a public PC, you can create a new folder, start LibreOffice with a parameter -env:UserInstallation= pointing to this new folder and delete this folder after your work is done. That will erase all backups of the documents too.
You are not the only one who has concerns regarding privacy, read fdo#61174 and fdo#74834.
If it’s a Linux system, -env:UserInstallation=/dev/null works should work treats. I don’t have a Linux system to test that now, though, so it can be wrong.
It is worth noting that “-env:UserInstallation is not considered an end-user feature” (source). The correct form is: -env:UserInstallation=file:///path/to/dir note however that /dev/null will not work as it is owned by root and LO requires write permission to the location. I was originally getting a Java framework error (Error in function createSettingsDocument (elements.cxx).) from not using the correct form.