Assigning a virtual desktop to a monitor in Windows 10

Is there a way to assign a virtual desktop to a monitor in Windows 10 (i.e. have every monitor show a different VD)?

Unfortunately not with the windows 10 feature. Each virtual desktop contains all of your monitors. So when you switch to another virtual desktop you are switching to a new virtual desktop that spans all of your monitors.

Maybe one of the third party solutions can do this and run on Windows 10.

I may be late to the party, but there is a workaround that can get near what you want to do:

Type Win + Tab to show up the Multiple Desktops panel also showing windows of the current desktop. Right click on one of them and you can choose either "Show this window on all desktops" or "Show windows from this app on all desktops". You can now switch desktop and they'll stick to the screen.
Afaik, if you choose the 2nd option, it will remember your choice even if you close all windows from the app at one point.

hope it helps

You can also purchase a software called Actual Multiple Monitors.

It provides several helpful features but, IMO, the best of these features is providing each monitor a separate taskbar.

From the link above:

Actual Multiple Monitors improves Windows® user interface when working with several monitors at once. Install Actual Multiple Monitors to get such essential controls as Taskbar, Start menu, system tray and Task Switcher on each connected display, quickly allocate windows between monitors (either manually or automatically), improve the look-and-feel of your desktop with the multi-monitor desktop wallpaper and screen saver, switch your laptop between internal display and external displays in a click with desktop profiles.

Although it doesn't feel as natural as using a native Windows functionality and requires some initial tweaking around to make using it feel more comfortable, it's still good enough to boost productivity to a considerable extent.