[ajb]

If lldp proves inconvenient, pi's also have a unique cpu-id, which can be found in /proc/cpuinfo

I think something similar exists on most processors

[jagged-chisel]

How does cpu-id map to physical location? If I move it from a closet on the first floor, to a rack in the basement, how does knowing the cpu-id help?

[ajb]

You would use CPU id by having the vanilla image display its ID (or perhaps some more humanly readable derived name) until assigned something to display. It won't know that it's moved, that's an advantage of the port method.

I mentioned it because the OP was going to use Mac addresses in a similar way, and only didn't because the Mac addresses of her machines were unstable.