Labeling of trademark images with Vienna codes from the Vienna classification is a manual process carried out by domain experts by searching trademark image databases using specific keywords. Manual labeling is both a time-consuming and error-prone process. Therefore, in this paper, we investigate how deep learning techniques can improve and automate labeling of new unlabeled trademark images. Three different deep learning models, namely CNN, LSTM and GRU, are trained and tested on a collected dataset composed of 14,500 unique logos extracted from the European Union Intellectual Property Office Open Data Portal. A set of controlled experiments establishing baseline results on the dataset showed that CNN outperforms the other two models in terms of both accuracy and training time. The experimental results also suggest that deep learning models are an important tool that can be applied by Intellectual Property Offices in real-world applications to automate the trademark image classification task.