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For the past thirty years, public libraries have been involved in digitising the heritage they preserve. The digital objects generated in this way are included in digital libraries that are supposed to broaden the audience for heritage. This paper looks at the name given to these digital systems in France, and what is expected of them. Why and how should a heritage digital library be named? An analysis of 32 municipal libraries shows that the name exploits a variety of imaginations relating to territorial identity and shared representations of heritage, as well as technological innovation. It also shows that these naming practices are still highly empirical, and that libraries are finding it difficult - or unwilling - to adopt a genuine branding strategy.‪