You don't actually need to label them you just need all the prisoners to be able to memorize which name is associated with which box, Alice's box is the first on the left, Bob's the second etc... Then when Zach. Z. Z. Vanderwall opens "his box" and finds the name Bob he follows procedure.

You need a minimal perfect hash function but it's a thing that can be done, especially because prisoners in these sort of conundrums always have fantastic memories and mental math facility.

https://en.wikipedia.org/wiki/Perfect_hash_function#Minimal_...