Is the teacher the recipient of the free stay or is the free stay the experience that's being auctioned off (and the money goes to support the teacher/school)? It'd be a little odd if the teachers were spending their money on this (charity?) auction.

All that said, I'd try explaining the circumstances to your concierge so they can make a note, and also call the hotel on the day of the reservation and make sure that they know this is intended to be an anonymous gift for a school fundraiser. The person checking them in has no reason to disclose your identity and it's not displayed on the bill. Also, the hotel may even go the extra mile to offer a nicer upgrade if a premium suite is available. Hotels and staff like to be part of "feel good" initiatives, especially when they don't cost the hotel anything.