This is one of the behaviors of Safari that I have always disliked as compared to almost all other browsers. I have never used pinned tabs in Safari (and now Orion) because of this.
As far as a suggested option name and placement, my suggestion would be "Pin tabs to all windows" or conversely "Pin tabs to current window only" as the label and append it to the "Tabs:" options within "Appearance".
To me, when "Pin tabs to current window only" is enabled, pinned tabs behave exactly like non-pinned tabs but displayed to the left/top of non-pinned tabs with just the icon as they do now. As far as my personal expectation, there's nothing more specific to it. Different pinned tabs in different windows would behave exactly like different non-pinned tabs in different windows. Perhaps I misunderstand the issue/question.