The success of multi-modal foundational models can be partly attributed to their diverse, billions scale training data. By nature, web data contains human faces and descriptions of individuals. Thus, these models pose potentially widespread privacy issues. Recently, identity membership inference attacks (IMIAs) against the CLIP model showed that membership of an individual's name and image within training data can be reliably inferred. This work formalizes the problem of identity extraction, wherein an attacker can reliably extract the names of individuals given their images only. We provide the following contributions (i) we adapt a previous IMIA to the problem of selecting the correct name among a large set and show that the method scales to millions of names (ii) we design an attack that outperforms the adapted baseline (iii) we show that an attacker can extract names via optimization only. To demonstrate the interest of our framework, we show how identity extraction can be used to audit model privacy. Indeed, a family of prominent models that advertise blurring faces before training to protect privacy is still highly vulnerable to attack.