When stowing, you still need to specify what to stow or unstow. With the --dir and --target options, all you're doing is to tell stow where packages are to be found and where they are to be linked to, but you don't tell it what to do.
In your case, either of these would work:
stow --target="$HOME/.dotfiles/test" --dir="$HOME/.dotfiles/.common-dotfiles" .
stow --target="$HOME/.dotfiles/test" --dir="$HOME/.dotfiles" .common-dotfiles
(I would personally prefer the second option as it refers to .common-dotfiles as the package to stow from "$HOME/.dotfiles", while the first variation refers to "$HOME/.dotfiles/.common-dotfiles" as the directory containing packages.)
You can also explicitly tell stow that you want to stow a particular package with --stow (or -S):
stow --target="$HOME/.dotfiles/test" --dir="$HOME/.dotfiles" --stow .common-dotfiles