Automatic vertebra localization and identification in CT scans is important for numerous clinical applications. Much progress has been made on this topic, but it mostly targets positional localization of vertebrae, ignoring their orientation. Additionally, most methods employ heuristics in their pipeline that can be sensitive in real clinical images which tend to contain abnormalities. We introduce a simple pipeline that employs a standard prediction with a U-Net, followed by a single graph neural network to associate and classify vertebrae with full orientation. To test our method, we introduce a new vertebra dataset that also contains pedicle detections that are associated with vertebra bodies, creating a more challenging landmark prediction, association and classification task. Our method is able to accurately associate the correct body and pedicle landmarks, ignore false positives and classify vertebrae in a simple, fully trainable pipeline avoiding application-specific heuristics. We show our method outperforms traditional approaches such as Hungarian Matching and Hidden Markov Models. We also show competitive performance on the standard VerSe challenge body identification task.