I agree. When our kids were young, we always had a safeword. If I absolutely had to send a neighbor or somebody they weren't quite familiar with, the person would tell them the safe word and they would know it was ok to go with them.Kids should be instructed never to go with anyone who says "Mom sent me to pick you up," even if they address the kid by name, no matter what the person tells them has happened. But I get why they don't want names on backpacks or clothing, and I don't think the teacher should have written on the kids' backpacks, even if there was a requirement that the kids' belongings be labeled. Use a sticker, then tell the parent they need some sort of label.
If somebody said "Hey Johnny, your mom sent me to pick you up" and did not say the safe word, the kids knew that they were never to go with that person.
As for teachers writing with sharpies on personal belongings -NO NO NO. Send a note and ask the parent to put the name on the backpack. As for the wallet incident, again, NO NO NO. If the parent does not put the name on it and it is lost, their fault. But the teacher should never permanently mark a personal item without the parent's permission.
I worked in a kindergarten for years. The kids had hooks with their names on it. The teacher could easily find a child's backpack. No need to deface personal property. If the teacher absolutely needs the names on it, the suggestion of masking tape and the name easily solves the problem. That is what our football coaches do to helmets and pads.
I would be asking the school to replace the backpack.