While recent advances in 3D-aware Generative Adversarial Networks (GANs) have aided the development of near-frontal view human face synthesis, the challenge of comprehensively synthesizing a full 3D head viewable from all angles still persists. Although PanoHead proves the possibilities of using a large-scale dataset with images of both frontal and back views for full-head synthesis, it often causes artifacts for back views. Based on our in-depth analysis, we found the reasons are mainly twofold. First, from network architecture perspective, we found each plane in the utilized tri-plane/tri-grid representation space tends to confuse the features from both sides, causing mirroring'' artifacts (e.g., the glasses appear in the back). Second, from data supervision aspect, we found that existing discriminator training in 3D GANs only focuses on the quality of the rendered image itself, and does not care about its plausibility with the perspective from which it was rendered. This makes it possible to generateface'' in the non-frontal view, due to its easiness to fool the discriminator. In response, we propose SphereHead, a novel tri-plane representation in the spherical coordinate system that fits the human head's geometric characteristics and efficiently mitigates many of the generated artifacts. We further introduce a view-image consistency loss for the discriminator to emphasize the correspondence of the camera labels and the images. The combination of these efforts results in visually superior outcomes with significantly fewer artifacts. Our code and dataset is publicly available at https://lhyfst.github.io/spherehead/.