Intrigued by geneticists’ framing of new gene names as somehow devoid of meaning, I set out to explore how patients and families make sense of naming practices in the field of genomic medicine. The aim for ever-more precise disease categorisation has resulted in names for medical conditions that are more akin to car-licence plates, such as DPF2 and G246A. Conducting fieldwork in Denmark, I followed the introduction of personalised medicine—that is the aim to tailor prevention, diagnosis, and treatment to the individual based on genomic and other data—in the field of rare diseases and diabetes. Engaging with theories of naming, spatialisation and serialisation, I suggest that it is exactly because of their unsettled meaning and presupposed lack of history that new gene names provide patients extra room for creative identity work. I argue that some patients and families use the new genetic disease labels to escape unwanted moral regimes, relocating disease aetiology from a moralised landscape to a ‘molecularised’ genetic one. I discuss how practices of serialisation enable patients to feel recognised as unique persons. In conclusion, I suggest that while the new genetic names may not stigmatise, they do change the patients’ idea of who they are in surprising ways, some of which the geneticists had not anticipated.