ChatGPT is a conversational agent built on a large language model. Trained on a significant portion of human output, ChatGPT can mimic people to a degree. As such, we need to consider what social identities ChatGPT simulates (or can be designed to simulate). In this study, we explored the case of identity simulation through Japanese first-person pronouns, which are tightly connected to social identities in intersectional ways, i.e., intersectional pronouns. We conducted a controlled online experiment where people from two regions in Japan (Kanto and Kinki) witnessed interactions with ChatGPT using ten sets of first-person pronouns. We discovered that pronouns alone can evoke perceptions of social identities in ChatGPT at the intersections of gender, age, region, and formality, with caveats. This work highlights the importance of pronoun use for social identity simulation, provides a language-based methodology for culturally-sensitive persona development, and advances the potential of intersectional identities in intelligent agents.