[caseyohara]

I'm curious, what would you call it instead?

Safari and Firefox call it "Private Browsing". I wonder if that's any better.

[bee_rider]

Maybe the button could be something along the lines of “Keep website history.”

[KeplerBoy]

More like "pause website history"

[bee_rider]

It could be a toggle, which actually would probably be more representative of the significance. Having a whole “mode” makes it seem way bigger of a difference than it actually is.