(T)ACSA tasks, including aspect-category sentiment analysis (ACSA) and targeted aspect-category sentiment analysis (TACSA), aims at identifying sentiment polarity on predefined categories. Incremental learning on new categories is necessary for (T)ACSA real applications. Though current multi-task learning models achieve good performance in (T)ACSA tasks, they suffer from catastrophic forgetting problems in (T)ACSA incremental learning tasks. In this paper, to make multi-task learning feasible for incremental learning, we proposed Category Name Embedding network (CNE-net). We set both encoder and decoder shared among all categories to weaken the catastrophic forgetting problem. Besides the origin input sentence, we applied another input feature, i.e., category name, for task discrimination. Our model achieved state-of-the-art on two (T)ACSA benchmark datasets. Furthermore, we proposed a dataset for (T)ACSA incremental learning and achieved the best performance compared with other strong baselines.