|Many of the commonly used datasets for face recognition development are collected from the internet without proper user consent. Due to the increasing focus on privacy in the social and legal frameworks, the use and distribution of these datasets are being restricted and strongly questioned. These databases, which have a realistically high variability of data per identity, have enabled the success of face recognition models. To build on this success and to align with privacy concerns, synthetic databases, consisting purely of synthetic persons, are increasingly being created and used in the development of face recognition solutions. In this work, we present a three-player generative adversarial network (GAN) framework, namely IDnet, that enables the integration of identity information into the generation process. The third player in our IDnet aims at forcing the generator to learn to generate identity-separable face images. We empirically proved that our IDnet synthetic images are of higher identity discrimination in comparison to the conventional two-player GAN, while maintaining a realistic intra-identity variation. We further studied the identity link between the authentic identities used to train the generator and the generated synthetic identities, showing very low similarities between these identities. We demonstrated the applicability of our IDnet data in training face recognition models by evaluating these models on a wide set of face recognition benchmarks. In comparison to the state-of-the-art works in synthetic-based face recognition, our solution achieved comparable results to a recent rendering-based approach and outperformed all existing GAN-based approaches. The training code and the synthetic face image dataset are publicly available.