See this here? I am trying to find something like it so that I can create wall riser extensions for my cubicle at work. I'd cut some lengths of 3/16"-thick board, attach to them these brackets, and then mount them on the inserts (or whatever those are called). The thing is that I don't know what the end pieces of these brackets are called. If I knew, I could execute a proper Google search to find more of them, but I don't, so I can't.
A medium duty, standard single slot, blade bracket?
Another option might be removing the plastic caps off the uprights and slide something down there; put 'legs' on the board and slip it in. Isn't that how some partitions with glass tops work?
I doubt there is a common name for that mount but first thing you will need to do is find out the manufacture of the cubicle system. Once you have that, you can then start searching for brackets or mounts for that system. I quick google search, and it came up with a couple of items like that under the name of shelf bracket and tackboard clip.
I just did a search for "slot mount bracket cubicle" when I found your picture. Looks like you & I have the same problem.
Based on the results I got, there are different manufacturers, and their slot dimensions are not universal. However, since you have an existing bracket to measure, you should be able to figure out which manufacturer yours is.
The results I received included lots of manufacturer names and dimensions. Use terms like 'fits steelcase 900', or 'fits 1" on center', or '3/4" with 1.25" gap', etc. to do a more deailed search.