Goods, styles, ideologies are adopted by society through various mechanisms. In particular, adoption driven by innovation is extensively studied by marketing economics. Mathematical models are currently used to forecast sales of innovative goods. Inspired by the theory of diffusion processes developed for marketing economics, we propose a modelling framework for the mechanism of fashion, which we apply to first names. Analyses of French, Dutch, and US national databases validate our modelling approach for thousands of first names, covering, on average, more than 50\% of the yearly incidence in each database. In these cases, it is thus possible to study how first names become popular and when they run out of fashion. Furthermore, we uncover a clear distinction between popularity and fashion: less popular names, typically not included in studies of fashion, may be driven by fashion, as well.