Different speakers often produce different names for the same object or entity (e.g., "woman" vs. "tourist" for a female tourist). The reasons behind variation in naming are not well understood. We create a Language and Vision dataset for Mandarin Chinese that provides an average of 20 names for 1319 naturalistic images, and investigate how familiarity with a given kind of object relates to the degree of naming variation it triggers across subjects. We propose that familiarity influences naming variation in two competing ways: increasing familiarity can either expand vocabulary, leading to higher variation, or promote convergence on conventional names, thereby reducing variation. We find evidence for both factors being at play. Our study illustrates how computational resources can be used to address research questions in Cognitive Science.