Many concepts in the medical literature are named after persons. Frequent ambiguities and spelling varieties, however, complicate the automatic recognition of such eponyms with natural language processing (NLP) tools. Recently developed methods include word vectors and transformer models that incorporate context information into the downstream layers of a neural network architecture. To evaluate these models for classifying medical eponymy, we label eponyms and counterexamples mentioned in a convenience sample of 1,079 Pubmed abstracts, and fit logistic regression models to the vectors from the first (vocabulary) and last (contextualized) layers of a SciBERT language model. According to the area under sensitivity-specificity curves, models based on contextualized vectors achieved a median performance of 98.0% in held-out phrases. This outperformed models based on vocabulary vectors (95.7%) by a median of 2.3 percentage points. When processing unlabeled inputs, such classifiers appeared to generalize to eponyms that did not appear among any annotations. These findings attest to the effectiveness of developing domain-specific NLP functions based on pre-trained language models, and underline the utility of context information for classifying potential eponyms.