In recent years, there has been significant growth in the commercial applications of generative models, licensed and distributed by model developers to users, who in turn use them to offer services. In this scenario, there is a need to track and identify the responsible user in the presence of a violation of the license agreement or any kind of malicious usage. Although there are methods enabling Generative Adversarial Networks (GANs) to include invisible watermarks in the images they produce, generating a model with a different watermark, referred to as a fingerprint, for each user is time- and resource-consuming due to the need to retrain the model to include the desired fingerprint. In this paper, we propose a retraining-free GAN fingerprinting method that allows model developers to easily generate model copies with the same functionality but different fingerprints. The generator is modified by inserting additional Personalized Normalization (PN) layers whose parameters (scaling and bias) are generated by two dedicated shallow networks (ParamGen Nets) taking the fingerprint as input. A watermark decoder is trained simultaneously to extract the fingerprint from the generated images. The proposed method can embed different fingerprints inside the GAN by just changing the input of the ParamGen Nets and performing a feedforward pass, without finetuning or retraining. The performance of the proposed method in terms of robustness against both model-level and image-level attacks is also superior to the state-of-the-art.