This article examines the work of internet activist and artist Paolo Cirio, whose practice intersects with matters of copyright, privacy, transparency and corporate finance. His project Loophole for All, for example, exposes the practice of tax evasion in the Cayman Islands by counterfeiting Certificate of Incorporation documents. An important aspect of Cirio’s work is how he names himself in the process. Placed within our contemporary ‘data turn’, his work is framed critically in this article in terms of a ‘new structuralist’ account of culture and society. The article attends to the view that power increasingly comes through the algorithm, but argues that we risk reifying so-called generative rules, which may simply be algorithms out of sight. Cirio’s art practice helps focus on what it means to make a critique of contemporary and ubiquitous algorithm structures. As part of this, the article considers how ‘anonymity’ underlies subversive art practices of the 20th century and contemporary protest groups, but that this anonymity arguably undermines attempts to effect change.