Young children often find it difficult to learn two labels for a single object. However, there is a great deal of variability across studies in children’s bias to reject second labels. In this study, we investigated three possible factors affecting this variability including age, task, and parental input in a cross-sectional sample of children from 12- to 28-months-old. We show that children reject second labels differently depending on their age, task demands, and the amount and type of parental input. Importantly, there is also a correlation between the ways in which parent’s use second labels and children’s acceptance of first and second labels for objects. These results suggest that both previous experience and the task at hand determine children’s learning of second labels.