[Update: creator here 👋 - I have pulled this app from the App Store because it's a free app that I currently don't have a great way to test on Monterey, as I don't own hardware that can run it (I have a 2014 MBP). That said, users have emailed me still wanting it, and I have selectively put it in the store every week or two for a short amount of time so they can grab it. If you are interested in knowing when those windows are, shoot me an email via the support tab on the homepage https://currentkey.com through an email or twitter DM. But also, Apple should just go ahead and support named Desktops natively, they're inevitably going to do so eventually - as all other OS platforms do, and it should be sooner rather than later. Thanks!]
There's an app (in the Mac App Store) that lets you name Spaces via the menubar.
It's different than naming them in Mission Control (they don't show up there), but the names are persistent and the app lets you set a custom icon in the menubar per Space, for a quick visual reference of what Space you're in. Why not in Mission Control? Because macOS public APIs are limited, and this app is delivered via the App Store.
It may be what you're looking for. Full disclaimer: I'm the developer of the app, called CurrentKey Stats. It's completely free in the App Store.
The app also lets you jump directly to another (named) Space via its dropdown menu or via global hotkeys. B/c Apple lets you have up to 16 Spaces per screen, this is handy in navigating between them.