Public perceptions of a brand is critical to its performance. While social media has demonstrated a huge potential to shape public perceptions of brands, existing tools are not intuitive and explanatory for domain users to use as they fail to provide a comprehensive analysis framework for perceptions of brands. In this paper, we present SocialBrands, a novel visual analysis tool for brand managers to understand public perceptions of brands on social media. Social-Brands leverages brand personality framework in marketing literature and social computing approaches to compute the personality of brands from three driving factors (user imagery, employee imagery, and official announcement) on social media, and construct an evidence network explaining the association between brand personality and driving factors. These computational results are then integrated with new interactive visualizations to help brand managers understand personality traits and their driving factors. We demonstrate the usefulness and effectiveness of SocialBrands through a series of user studies with brand managers in an enterprise context. Design lessons are also derived from our studies.