The rise of precision medicine has led to an unprecedented focus on human biological material in biomedical research. In addition, rapid advances in stem cell technology, regenerative medicine and synthetic biology are leading to more complex human tissue structures and new applications with tremendous potential for medicine. While promising, these developments also raise several ethical and practical challenges which have been the subject of extensive academic debate. These debates have led to increasing calls for longitudinal governance arrangements between tissue providers and biobanks that go beyond the initial moment of obtaining consent, such as closer involvement of tissue providers in what happens to their tissue, and more active participatory approaches to the governance of biobanks. However, in spite of these calls, such measures are being adopted slowly in practice, and there remains a strong tendency to focus on the consent procedure as the tool for addressing the ethical challenges of contemporary biobanking. In this paper, we argue that one of the barriers to this transition is the dominant language pervading the field of human tissue research, in which the provision of tissue is phrased as a ‘donation’ or ‘gift’, and tissue providers are referred to as ‘donors’. Because of the performative qualities of language, the effect of using ‘donation’ and ‘donor’ shapes a professional culture in which biobank participants are perceived as passive providers of tissue free from further considerations or entitlements. This hampers the kind of participatory approaches to governance that are deemed necessary to adequately address the ethical challenges currently faced in human tissue research. Rather than reinforcing this idea through language, we need to pave the way for the kind of participatory approaches to governance that are being extensively argued for by starting with the appropriate terminology.