Neural Network (NN) architectures are used more and more to model large amounts of data, such as text data available online. Transformer-based NN architectures have shown to be very useful for language modelling. Although many researchers study how such Language Models (LMs) work, not much attention has been paid to the privacy risks of training LMs on large amounts of data and publishing them online. This paper presents a new method for anonymizing a language model by presenting the way in which MedRoBERTa.nl, a Dutch language model for hospital notes, was anonymized. The two step method involves i) automatic anonymization of the training data and ii) semi-automatic anonymization of the LM's vocabulary. Adopting the fill-mask task where the model predicts what tokens are most probable to appear in a certain context, it was tested how often the model will predict a name in a context where a name should be. It was shown that it predicts a name-like token 0.2% of the time. Any name-like token that was predicted was never the name originally presented in the training data. By explaining how a LM trained on highly private real-world medical data can be safely published with open access, we hope that more language resources will be published openly and responsibly so the community can profit from them.