Is there a name for this kind of comparator?
does this have a name?


Yes, it is a window comparator even though you think it isn't. Regular window comparators have one "variable" input but there's nothing wrong with the "fixed" input being variable too. Consider this "regular" circuit: -



If the middle of the three resistors were, in fact, two resistors in series (with the new input feeding the centre-point) then you get a window (magnitude) comparator. Depending on precisely how you want this to work you can make the two outer resistors into a current source and a current sink and you could even use something like a TL431 across the full width of the middle resistor to define precise thresholds above and below the new reference input.

It's still a window comparator.