Across cultures, names tell a lot about their bearers as they carry deep personal and cultural significance. Names also serve as powerful signals of gender, race, and status in the social hierarchy - a pecking order in which individual positions shape others' expectations on their perceived competence and worth. With the widespread adoption of LLMs and as names are often an input for LLMs, it is crucial to evaluate whether LLMs may sort people into status positions based on first and last names and, if so, whether it is in an unfair, biased fashion. While prior work has primarily investigated biases in first names, little attention has been paid to last names and even less to the combined effects of first and last names. In this study, we conduct a large-scale analysis of name variations across 5 ethnicities to examine how AI exhibits name biases. Our study investigates three key characteristics of inequality and finds that LLMs reflect and reinforce status hierarchies based on names that signal gender and ethnicity as they encode differential expectations of competence, leadership, and economic potential. Contrary to the common assumption that AI tends to favor Whites, we show that East and, in some contexts, South Asian names receive higher rankings. We also disaggregate Asians, a population projected to be the largest immigrant group in the U.S. by 2055. Our results challenge the monolithic Asian model minority assumption, illustrating a more complex and stratified model of bias. Gender moderates biases, with girls facing unfair disadvantages in certain racial groups. Additionally, spanning cultural categories by adopting Western first names improves AI-perceived status for East and Southeast Asian students, particularly for girls. Our findings underscore the importance of intersectional and more nuanced understandings of race, gender, and mixed identities in the evaluation of LLMs.