In many cases, what is commonly known as "mistaken," "lost" or "stolen" identity is actually an example of a social class system at work, in which the public expression of an individual's attributes has been secretly manipulated for a political or social purpose
This internally agreed upon system, in which a member's identity can be temporary, variable, and sometimes interchangeable, is one aspect of a covert simulation, or game, which is played simultaneous with the process of exoteric reality.
A good model of such impermanence in externally redefined identity comes from within the clandestine intelligence services, such as the CIA, where even the legitimating overt "cover" roles are shifted around every three years on average.
This type of alteration to a publicly perceived identity is distinct from the process of one's own internal self-reinvention---an ability available to anyone---as it requires the connivance of at least some parts of the political and social order. And with enough support from those establishment structures, the creation of an entirely fictitious identity from scratch is even possible, as well as the assumption or theft of someone else's pre-existing identity, whether they be still living or dead.
In the same vein, identity can be shared, split-off, blended, or morphed