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Personalized federated learning (FL) facilitates collaborations between multiple clients to learn personalized models without sharing private data. The mechanism mitigates the statistical heterogeneity commonly encountered in the system, i.e., non-IID data over different clients. Existing personalized algorithms generally assume all clients volunteer for personalization. However, potential participants might still be reluctant to personalize models since they might not work well. In this case, clients choose to use the global model instead. To avoid making unrealistic assumptions, we introduce the personalization rate, measured as the fraction of clients willing to train personalized models, into federated settings and propose DyPFL. This dynamically personalized FL technique incentivizes clients to participate in personalizing local models while allowing the adoption of the global model when it performs better. We show that the algorithmic pipeline in DyPFL guarantees good convergence performance, allowing it to outperform alternative personalized methods in a broad range of conditions, including variation in heterogeneity, number of clients, local epochs, and batch sizes.