I don't know if this was available at the time of these posts, but I was looking for this information today and noticed at the bottom of the profile settings page, there's an option to create a desktop shortcut to the profile.
I unpinned Vivaldi from the taskbar and then created the shortcut. It actually created a shortcut to both of my profiles, which I wanted anyway.
It puts a mini avatar on the Vivaldi icon on the taskbar for easy ID, so that's great.
I right-clicked the shortcuts and pinned them to the taskbar.
vivaldi://settings/manageProfile