The emergence of unveiling human-like behaviors in Large Language Models (LLMs) has led to a closer connection between NLP and human psychology. Scholars have been studying the inherent personalities exhibited by LLMs and attempting to incorporate human traits and behaviors into them. However, these efforts have primarily focused on commercially-licensed LLMs, neglecting the widespread use and notable advancements seen in Open LLMs. This work aims to address this gap by employing a set of 12 LLM Agents based on the most representative Open models and subject them to a series of assessments concerning the Myers-Briggs Type Indicator (MBTI) test and the Big Five Inventory (BFI) test. Our approach involves evaluating the intrinsic personality traits of Open LLM agents and determining the extent to which these agents can mimic human personalities when conditioned by specific personalities and roles. Our findings unveil that $(i)$ each Open LLM agent showcases distinct human personalities; $(ii)$ personality-conditioned prompting produces varying effects on the agents, with only few successfully mirroring the imposed personality, while most of them being ``closed-minded'' (i.e., they retain their intrinsic traits); and $(iii)$ combining role and personality conditioning can enhance the agents' ability to mimic human personalities. Our work represents a step up in understanding the dense relationship between NLP and human psychology through the lens of Open LLMs.