I am a quilt teacher. I instruct ALL my students to put their name, an address label or just write with a sharpie. I explain that we all have look-a-likes, and all can get misplaced...
You could try putting a list of what you bring in your bagm box, and announce prior to end of class that you need to read it off to insure you are not taking home anyone elses belongings.
Good Luck, and sorry we cannot trust our fellow quilters. Sad, very sad.