I found some pocket over-the-door shoe holders, and I attached index cards to them with students' names. After I grade any formative or summative assessments, I stick them in each cubby, and I can do this after school or whenever I have the time. Students are excited when they come in to see that they have "mail." They know this is the first thing they should go to before they find their seat.
A major rule is that students are not allowed to look in anyone else's cubby. I fold assessments and place them grade down so it would be hard to peek at someone else's grade.
I think next year, I will have them design their own index cards. I did that a number of years ago when I first used the shoe holders, and students would actually write notes to other students and put them in cubbies as well--even from other classes! I'm not sure why I gave them up for a few years and put them in storage; I think it was because it does take a bit longer than to put them out on the desks. One advantage though is that now you can do it at your leisure, and not just right before class.
Finally, I had another idea: if I catch a student looking at their phone in class, it goes in his/her cubby for the rest of the period. Oh--and I alphabetize the index cards...but I had to switch a few tall students with shorter ones, so keep that in mind if you do this!
It is also good for when students are absent and you have a handout for them--just put it in their "mailbox." And if I need to see a student after class, I can just leave them a note. How many times I have forgotten to tell a student I need to see them, only to remember right after they walked out the door?!
What do you see yourself using these for?