The example of such an unthinkable or unimaginable thing for a person could be non-existence, therefore argument against existence seems to be so absurd. Aren't we calling such things axioms or postulates?
Such a thing is not in general an axiom or postulate. Such an idea can be complex and non-foundational. Humans may not be able to actually imagine that there are countably many Real numbers. But to get to that point requires a lot of leverage. No one would consider that an axiom.
More formally, very few such things are axioms. For if you had two or more ideas that cannot be imagined to be false, their combination would also be such a thing. The combination of two axioms is never an axiom.
I think that what you are after are simply necessary propositions, statements in the modality of "must", the content of the standard modal logic selected by the 'box' operator, facts true in all possible worlds (however one chooses to name this content.)
If you mean a specific person, and not a general person, this is the variant of that modality where the relevant attached context for necessity (or set of possible worlds, or visibility filter on the possible worlds (again depending on your model of a modal)) is determined by that individual's mental configuration rather than by "natural" possibility.