Modulation recognition is a fundamental task in communication systems as the accurate identification of modulation schemes is essential for reliable signal processing, interference mitigation for coexistent communication technologies, and network optimization. Incorporating deep learning (DL) models into modulation recognition has demonstrated promising results in various scenarios. However, conventional DL models often fall short in online dynamic contexts, particularly in class incremental scenarios where new modulation schemes are encountered during online deployment. Retraining these models on all previously seen modulation schemes is not only time-consuming but may also not be feasible due to storage limitations. On the other hand, training solely on new modulation schemes often results in catastrophic forgetting of previously learned classes. This issue renders DL-based modulation recognition models inapplicable in real-world scenarios because the dynamic nature of communication systems necessitate the effective adaptability to new modulation schemes. This paper addresses this challenge by evaluating the performance of multiple Incremental Learning (IL) algorithms in dynamic modulation recognition scenarios, comparing them against conventional DL-based modulation recognition. Our results demonstrate that modulation recognition frameworks based on IL effectively prevent catastrophic forgetting, enabling models to perform robustly in dynamic scenarios.