Never before have individuals known so much about their behavior—yet understood themselves so little outside algorithmic feedback. For Gen Z, whose everyday experiences are filtered through data and platforms, algorithmic presence has become a defining element of self-perception. This paper addresses a central puzzle: how identity reflection has shifted from social mirrors to algorithmic ones, making data itself a participant in self-definition. Building on Dutton and Dukerich's (1991) framework of the identity-image interface, this study extends the model from the organizational to the individual-algorithm context. It theorizes the Algorithmic Identity Negotiation Process (AINP)—a dynamic in which algorithmic feedback acts as both mirror and audience in the construction of identity. To examine this process, the study employs the annual Spotify Wrapped as a bounded, reflexive ritual of data presentation uniquely suited to observing algorithmic self-reflection. Ten in-depth interviews with Gen Z users explore how individuals interpret, contest, and perform their data. Thematic analysis links their lived experiences to the AINP framework. Evidence shows that users confront an algorithmic mirror producing reactions of congruence or dissonance, trust or skepticism, and moments of self-discovery. Participants engaged in strategic impression-management—deciding what to share publicly—which then shaped a feedback loop of future "conscious listening." Unexpectedly, several treated the algorithm not as omniscient but as a fallible partner in self-representation. The study reframes identity negotiation for the algorithmic era, positioning data as an active medium in the identity-to-image conversion process. It advances identity theory by conceptualizing algorithmic identity negotiation as a contemporary mechanism of self-understanding and public performance.