Due to their situated nature, digital public displays have the potential to provide information and messages to large groups of people. However, in practice, non-customised content typically is not relevant to every passerby, while personalising information tailored to individuals is associated with privacy concerns. Previous research has identified mobile augmented reality as a promising method for keeping digital displays public, yet enabling customised views for interested passersby in a way that retains privacy. By building on this previous work, the aim of this paper is to understand user preferences for interacting with personalised information on digital public displays through their mobile device. The paper reports on a study that was conducted with a prototype augmented reality app and public display system. Findings from the study highlight the need for contextual personalisation based upon user activities and objectives at the time of the interaction. Additionally, interactions should be adaptable between public and covert, depending upon what the user wants to share. Based on these findings the paper presents a series of design implications for personalising public displays.