Manually creating concise and meaningful method names is often challenging and time-consuming for software engineers, especially for less experienced and non-native English speakers. They may find it easier to provide functional descriptions in their native languages; however, this practice results in inherent ambiguities (e.g., natural language, semantic gaps, cultural misinterpretations) and limited lexical overlap with English names. To address these challenges, this paper presentsLangInsightCraft, a novel context-rich prompt generation algorithm to guide LLMs in suggesting method names from cross-language functional descriptions. From the input description, it retrieves similar high-quality native examples and extracts key contextual elements (e.g., entities, actions, functionality scope) from descriptions of these examples, to overcome inherent ambiguities. It also generates a set of candidate method names for each example’s description, evaluates them against the example’s method name using edit-distance and a semantic similarity index, and ranks them by alignment score. Using these ranked names,LangInsightCraftgenerates an English textual explanation for each candidate name, which helps LLM handle the challenge of limited lexical overlap between English method names and non-English descriptions. Finally, it embeds these outputs, input and examples into a predefined prompt template to generate a context-rich prompt for LLM to generate the expected method name. Evaluated on 64,815 Java methods with English/Chinese descriptions,LangInsightCraftsubstantially outperformsRNN-att-Copy, improving exact-match by 54% and 122%, and decreasing edit-distance by 33% and 54%, on English and Chinese datasets respectively, while generalizing well across different LLMs.