Classifying logo images is a challenging task as they contain elements such as text or shapes that can represent anything from known objects to abstract shapes. While the current state of the art for logo classification addresses the problem as a multi‐class task focusing on a single characteristic, logos can have several simultaneous labels, such as different colours. This work proposes a method that allows visually similar logos to be classified and searched from a set of data according to their shape, colour, commercial sector, semantics, general characteristics, or a combination of features selected by the user. Unlike previous approaches, the proposal employs a series of multi‐label deep neural networks specialized in specific attributes and combines the obtained features to perform the similarity search. To delve into the classification system, different existing logo topologies are compared and some of their problems are analysed, such as the incomplete labelling that trademark registration databases usually contain. The proposal is evaluated considering 76,000 logos (seven times more than previous approaches) from the European Union Trademarks dataset, which is organized hierarchically using the Vienna ontology. Overall, experimentation attains reliable quantitative and qualitative results, reducing the normalized average rank error of the state‐of‐the‐art from 0.040 to 0.018 for the Trademark Image Retrieval task. Finally, given that the semantics of logos can often be subjective, graphic design students and professionals were surveyed. Results show that the proposed methodology provides better labelling than a human expert operator, improving the label ranking average precision from 0.53 to 0.68.