If a person hypothetically had duel citizenship and two passports with two different last names on those passports, could they enter the Schengen area, leave before the 90 days is up, then come back into the area with the different passport that has the different name for a renewed 90 days?
It depends what you mean by “could”. It is not allowed; If you read the relevant regulations, the entry refusal form, etc. candidly the maximum duration of authorized stay clearly applies to a person and I consider it obvious that border guards (and, if needed, the courts) would interpret it in that way.
But, as of writing this, there is no Schengen-wide database of entries and exits so no easy way for a border guard to notice the person was previously in the Schengen area during a routine interview/database lookup so even with the same last name you might get away with it. Even another passport from the same country could be enough.
However, there are many other ways to get caught: if you are staying/living in one place and the local police notices, if someone turns you in, etc.
Beyond that, since that person would be staying illegally anyway, I am not sure it makes sense to say that they are coming for “a renewed 90 days”. They are simply evading detection at the border but since they are illegally present from day one, any notion of “maximum duration of authorized stay” becomes moot.