We present two methods for learning the structure of personal names from unlabeled data. The first simply uses a few implicit constraints governing this structure to gain a toehold on the problem -- e.g., descriptors come before first names, which come before middle names, etc. The second model also uses possible coreference information. We found that coreference constraints on names improve the performance of the model from 92.6% to 97.0%. We are interested in this problem in its own right, but also as a possible way to improve named entity recognition (by recognizing the structure of different kinds of names) and as a way to improve noun-phrase coreference determination.