User identification is an essential step in creating a personalised long-term interaction with robots. This requires learning the users continuously and incrementally, possibly starting from a state without any known user. In this article, we describe a multi-modal incremental Bayesian network with online learning, which is the first method that can be applied in such scenarios. Face recognition is used as the primary biometric, and it is combined with ancillary information, such as gender, age, height, and time of interaction to improve the recognition. The Multi-modal Long-term User Recognition Dataset is generated to simulate various human-robot interaction (HRI) scenarios and evaluate our approach in comparison to face recognition, soft biometrics, and a state-of-the-art open world recognition method (Extreme Value Machine). The results show that the proposed methods significantly outperform the baselines, with an increase in the identification rate up to 47.9% in open-set and closed-set scenarios, and a significant decrease in long-term recognition performance loss. The proposed models generalise well to new users, provide stability, improve over time, and decrease the bias of face recognition. The models were applied in HRI studies for user recognition, personalised rehabilitation, and customer-oriented service, which showed that they are suitable for long-term HRI in the real world.