We develop a methodological framework that addresses both challenges. First, we propose list-powered Bayesian Improved Surname Geocoding (L-BISG), which derives calibrated group probabilities from group-specific name lists, including those generated synthetically by large language models (LLMs). Because these lists may contain unknown biases, we represent names using embeddings and apply a statistical correction based on proximal inference. Second, we propose Bayesian Instrumental Regression for Disparity Estimation (BIRDiE), which uses these probabilities to estimate disparities under an identification assumption that is often more credible than those underlying standard approaches. Across U.S. voter files, the full-count 1900 U.S. Census, and the Lebanese voter registry, we find that our framework, using LLM-generated name lists, produces accurate and well-calibrated group probabilities as well as precise disparity estimates comparable to those obtained by methods requiring name–race data.