From the beginning of the COVID-19 global pandemic, it became clear that the practices of naming the disease, its nature and its handling by the health authorities, the news media and the politicians had social and ideological implications. This article presents a sociosemiotic study of such practices as reflected in a corpus of headlines of eight newspapers of four countries in the early stages of the COVID-19 crisis. After an analysis of the institutional naming choices of the World Health Organization (WHO) and the International Committee on Taxonomy of Viruses, the study focuses on the changes in newspapers' naming patterns following the WHO's announcement of the disease name on 11 February 2020. A subsequent political controversy related to naming in the United States is then examined in reports of The New York Times and The Washington Post as a further illustration of how public discourses and perceptions can rapidly evolve in the context of health crises.