As innovation in deep learning continues, many engineers are incorporating Pre-Trained Models (PTMs) as components in computer systems. Some PTMs are foundation models, and others are fine-tuned variations adapted to different needs. When these PTMs are named well, it facilitates model discovery and reuse. However, prior research has shown that model names are not always well chosen and can sometimes be inaccurate and misleading. The naming practices for PTM packages have not been systematically studied, which hampers engineers' ability to efficiently search for and reliably reuse these models. In this paper, we conduct the first empirical investigation of PTM naming practices in the Hugging Face PTM registry. We begin by reporting on a survey of 108 Hugging Face users, highlighting differences from traditional software package naming and presenting findings on PTM naming practices. The survey results indicate a mismatch between engineers' preferences and current practices in PTM naming. We then introduce DARA, the first automated DNN ARchitecture Assessment technique designed to detect PTM naming inconsistencies. Our results demonstrate that architectural information alone is sufficient to detect these inconsistencies, achieving an accuracy of 94% in identifying model types and promising performance (over 70%) in other architectural metadata as well. We also highlight potential use cases for automated naming tools, such as model validation, PTM metadata generation and verification, and plagiarism detection. Our study provides a foundation for automating naming inconsistency detection. Finally, we envision future work focusing on automated tools for standardizing package naming, improving model selection and reuse, and strengthening the security of the PTM supply chain.