There is a growing interest in assessing the personality traits of Large language models (LLMs). However, traditional personality assessments based on self-report questionnaires may fail to capture their true behavioral nuances due to inherent biases and meta-knowledge contamination. This paper introduces a novel multi-observer framework for LLM personality assessment that draws inspiration from informant-report methods in psychology. Instead of relying solely on self-assessments, our approach employs multiple observer agents configured with a specific relationship context (e.g., family, friend, or workplace) to simulate interactive scenarios with a subject LLM. These observers engage in dialogues and subsequently provide ratings across the Big Five personality dimensions. Our experiments reveal that LLMs possess systematic biases in self-report personality ratings. Moreover, aggregating observer ratings effectively reduces non-systematic biases and achieves optimal reliability with 5-7 observers. The findings highlight the significant impact of relationship context on personality perception and demonstrate that a multi-observer paradigm yields a more robust and context-sensitive evaluation of LLM personality traits.