Large language models (LLMs) increasingly act on people's behalf: they write emails, buy groceries, and book restaurants. While the outsourcing of human decision-making to AI can be both efficient and effective, it raises a fundamental question: how does delegating identity-defining choices to AI reshape who people become? We study the impact of agentic LLMs on two identity-relevant outcomes: interpersonal distinctiveness - how unique a person's choices are relative to others - and intrapersonal diversity - the breadth of a single person's choices over time. Using real choices drawn from social-media behavior of 1,000 U.S. users (110,000 choices in total), we compare a generic and personalized agent to a human baseline. Both agents shift people's choices toward more popular options, reducing the distinctiveness of their behaviors and preferences. While the use of personalized agents tempers this homogenization (compared to the generic AI), it also more strongly compresses the diversity of people's preference portfolios by narrowing what they explore across topics and psychological affinities. Understanding how AI agents might flatten human experience, and how using generic versus personalized agents involves distinctiveness-diversity trade-offs, is critical for designing systems that augment rather than constrain human agency, and for safeguarding diversity in thought, taste, and expression.