Existing benchmarks that measure cultural adaptation in LLMs are misaligned with the actual challenges these models face when interacting with users from diverse cultural backgrounds. In this work, we introduce the first framework and benchmark designed to evaluate LLMs in realistic, multicultural conversational settings. Grounded in sociocultural theory, our framework formalizes how linguistic style - a key element of cultural communication - is shaped by situational, relational, and cultural context. We construct a benchmark dataset based on this framework, annotated by culturally diverse raters, and propose a new set of desiderata for cross-cultural evaluation in NLP: conversational framing, stylistic sensitivity, and subjective correctness. We evaluate today's top LLMs on our benchmark and show that these models struggle with cultural adaptation in a conversational setting.