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According to Lawvere 1984, codiscrete objects, i.e. those in the image of a right adjoint to a forgetful functor, may be though of as “chaotic” with repect to whatever mathematical structure was forgotten by the forgetful functor.
This convention matches/subsumes more-or-less common terminology such as chaotic topology or chaotic groupoid.
See also
The terminology “chaotic” for codiscrete objects goes back to
where it is used for Grothendieck topologies, from which it was, apparently, adapted to chaotic topologies on topological spaces.
General formalization of the concept in terms of right adjoints to forgetful functors is due to: