The need for long-term multi-object tracking (MOT) is growing due to the demand for analyzing individual behaviors in videos that span several minutes. Unfortunately, due to identity switches between objects, the tracking performance of existing MOT approaches decreases over time, making them difficult to apply for long-term tracking. However, in many real-world applications, such as in the livestock sector, it is possible to obtain sporadic identifications for some of the animals from sources like feeders. To address the challenges of long-term MOT, we propose a new framework that combines both uncertain identities and tracking using a Hidden Markov Model (HMM) formulation. In addition to providing real-world identities to animals, our HMM framework improves the F1 score of ByteTrack, a leading MOT approach even with re-identification, on a 10 minute pig tracking dataset with 21 identifications at the pen's feeding station. We also show that our approach is robust to the uncertainty of identifications, with performance increasing as identities are provided more frequently. The improved performance of our HMM framework was also validated on the MOT17 and MOT20 benchmark datasets using both ByteTrack and FairMOT. The code for this new HMM framework and the new 10-minute pig tracking video dataset are available at: https://github.com/ngobibibnbe/uncertain-identity-aware-tracking