I've totally been there and I needed a way to lessen the burden, especially the time it took to find each students name on the roster. This was my solution.
It's a file box with a hanging folder for each student. Each folder is labeled with numbers that correspond to each student. (That's another tip, number your students. Yes, that is 33 students in my class.) Students return their homework first thing in the morning right into their folder. They place them vertically, so they can be easily removed from the folders.
One of the class jobs is the "paper collector" whose job it is to take the papers from the file box, in order, then place the pile in the inbox on my desk. Here's my inbox.
The bottom box is the inbox and the top is the out box. Two students in the class have the job of "paper passer" whose job it is to pass back papers I've seen. ~You can see my current helpers need a little reminding.~
When students pass things in throughout the day, the same routine is followed. I rarely have a time when everyone in the class is handing something in at the same time because I work with groups most of the day. When the whole class does need to hand something in, I excuse them by tables while the rest of the class begins to transition to the next activity.
This method keeps student's papers in alphabetical order so that I can quickly find the students on the grade book list. It also keeps subjects together so I don't have to sort my papers or flip back and forth between subjects as I look at the papers.
I clip no-name papers to the board with a binder clip that hangs from a hook magnet. I'm always surprised though at how few of these papers get claimed. Students who have missing work seem to just prefer to redo the assignment rather than be bothered to look through the stack of nameless work. I recycle the pile at the end of each quarter.
I hope this tip is helpful to you and alleviates your burden when grading papers. Be sure to visit Maneuvering the Middle and her post about response systems.
Thanks to Shelley from Teaching in the Early Years for hosting and coordinating this event!