In this paper, we investigate the efficacy of large language models (LLMs) in obfuscating authorship by paraphrasing and altering writing styles. Rather than adopting a holistic approach that evaluates performance across the entire dataset, we focus on user-wise performance to analyze how obfuscation effectiveness varies across individual authors. While LLMs are generally effective, we observe a bimodal distribution of efficacy, with performance varying significantly across users. To address this, we propose a personalized prompting method that outperforms standard prompting techniques and partially mitigates the bimodality issue.