Racial disparity in academia is a widely acknowledged problem. The quantitative understanding of racial-based systemic inequalities is an important step towards a more equitable research system. However, because of the lack of robust information on authors' race, few large-scale analyses have been performed on this topic. Algorithmic approaches offer one solution, using known information about authors, such as their names, to infer their perceived race. As with any other algorithm, the process of racial inference can generate biases if it is not carefully considered. The goal of this article is to assess the extent to which algorithmic bias is introduced using different approaches for name-based racial inference. We use information from the U.S. Census and mortgage applications to infer the race of U.S. affiliated authors in the Web of Science. We estimate the effects of using given and family names, thresholds or continuous distributions, and imputation. Our results demonstrate that the validity of name-based inference varies by race/ethnicity and that threshold approaches underestimate Black authors and overestimate White authors. We conclude with recommendations to avoid potential biases. This article lays the foundation for more systematic and less-biased investigations into racial disparities in science.