Large language models (LLMs) have achieved remarkable performance across diverse natural language processing tasks, but concerns persist regarding their potential political biases. While prior research has extensively explored political biases in LLMs' text generation and perception, scant attention has been devoted to biases associated with media outlet names. In this study, we systematically investigate the presence of media outlet name biases in LLMs and evaluate their impact on downstream tasks, such as political bias prediction and news summarization. Our findings demonstrate that LLMs consistently exhibit biases toward the known political leanings of media outlets, with variations across model families and scales. We propose a novel metric to quantify media outlet name biases in LLMs and leverage this metric to develop an automated prompt optimization framework. This framework effectively mitigates media outlet name biases, offering a scalable approach to enhancing the fairness of LLMs in news-related applications.