|mkdir -p ~/.local/share/applications|
|cat << END > ~/.local/share/applications/vivaldi-private.desktop|
You may need to to a re-login before “Vivaldi (Private)” shows up as an item in the menus of your desktop environment.
To remove, just delete ‘~/.local/share/applications/vivaldi-private.desktop’
P.S. It is also worth noting that in popular Desktop Environments (i.e Gnome), the default desktop launcher for Vivaldi already has an entry to start a Vivaldi Private Window from the right click, context menu. The above is just an alternative or if your Desktop Environment of choice does not support desktop actions in desktop launcher files.