Yeah, naming things is really difficult!

The most truthful thing to call it would be "Temporary Session" but that name requires an understanding of what a 'session' is, in terms of a container that scopes your locally-stored browsing data. It's immediately comprehensible to tech-types, but probably meaningless to the average user.

There's not really any name that can accurately and succinctly describe what Incognito or private browsing actually does in a way that a normal person will understand from the name alone, but Amnesia mode is a good suggestion at one!