To the degree that your conception is object-oriented, in the deeper sense, it is not a problem.  Your object(s) know how to persist themselves and may be considered to be extensive over that persistence -- it is merely that their morphology has changed.

Are you trying to identify names in a known problem space (e.g. a space defined by the limits of the techniques used) or to identify the problem space that you're in?  For the latter, if you're going to generalise then perhaps you should also wave the specialisation of 'perfect' reproduction.  So, even more generally, what you seem to describing is a special case of morphogenesis in which a 'copy' is made, e.g. lazy evaluation and cached computation can be thought of as slices in that process.