Letter name knowledge (LNK) is a key predictor of later reading ability and has been emphasized strongly in recent educational policy. Studies of LNK have implicitly treated it as a unidimensional construct with all letters equally relevant to its measurement. However, some empirical research suggests that contextual factors can affect the measurement of LNK. In this study, we analyze responses from 909 children on measures of LNK using the Rasch model and its extensions, and consider two contextual factors: the format of assessment and the own-name advantage, which states that children are more likely to know letters in their own first names. Results indicate that both contextual factors have important impacts on measurement and that LNK does not meet the requirements of Rasch measurement even when accounting for the contextual factors. These findings introduce philosophical concerns for measurement of constrained skills which have limited content for assessment.