Can I rename Desktops?

 

Yes, and they are persistent. The app also lets you jump directly to another (named) Space via its dropdown menu. B/c Apple lets you have up to 16 Spaces per screen, this is handy in navigating between them. Because macOS APIs are limited, the names stay in the app and don't show up in Mission Control.

In this preview shot, you can see the option to jump directly to a Space (app calls them Rooms) via a dropdown. You can see time spent across them. And you can see one i'm currently in is called "Travel Research".

forStackExchange-roomsFeature.jpg

Does this app work with multiple monitors? i have the "displays have separate spaces" preference switched on in Mission Control prefs

 

Yes.

The app is designed to support multiple desktops.

Here is a quick video of multi-desktop use: