Current literature evaluates large language models (LLMs) on multilingual kinship understanding using multiple-choice benchmarks, treating it as a recognition problem. We instead prompt five open-weight LLMs to generate kinship terms in three non-Western languages (Hindi, Tamil, and Korean) across two communicative tasks, and pair this with a matched option-supported selection baseline. On identical relation–language cells, GPT-OSS120B selects the correct term in 90.67% of 75 valid cells but produces an accepted term in 36.00% of the corresponding attempts; Llama3.3-70B shows the same pattern (77.92% versus 24.24%). Since the four-option condition displays the candidate terms and does not require script production, the difference is interpreted as an evaluation-format gap rather than direct proof that lexical knowledge is intact. On explicitly specified L3 prompts, accuracy varies sharply, from GLM-5.1 at 72.29% to Llama3.3-70B at 24.24%. The paternal-lineage advantage is language-specific: it is large in Hindi, but weak or reversed in Korean, while Tamil shared-term pairs provide a control for measurement variation. These results show that culturally specific kinship generation remains difficult even when the relationship is explicitly stated and motivate generation-based evaluation alongside multiple-choice testing.