Speakers often use different names to refer to the same entity (e.g., "woman" vs. "tennis player"). We explore factors that affect naming variation for visually presented objects, analyzing a large dataset of object names with realistic images, and focusing on two factors: visual typicality (of objects and contexts) and name frequency. We develop a computational approach to estimate typicality, and not only study object names used by most annotators (top names), but also the second most used ones (alternative names). Our results show that variation increases for objects that are less typical for their top name, more typical for their alternative name, or whose top name has relatively low frequency. Context typicality does not show a general effect. Overall, we show that characteristics relating to name candidates beyond the top name are informative of naming variation, and the potential of using computational methods to inform models of human object naming.