Studying the complex quantum dynamics of interacting many-body systems is one of the most challenging areas in modern physics. Here, we use machine learning (ML) models to identify the symmetrized base states of interacting Rydberg atoms of various atom numbers (up to six) and geometric configurations. To obtain the data set for training the ML classifiers, we generate Rydberg excitation probability profiles that simulate experimental data by utilizing Lindblad equations that incorporate laser intensities and phase noise. Then, we classify the data sets using support vector machines (SVMs) and random forest classifiers (RFCs). With these ML models, we achieve high accuracy of up to 100% for data sets containing only a few hundred samples, especially for the closed atom configurations such as the pentagonal (five atoms) and hexagonal (six atoms) systems. The results demonstrate that computationally cost-effective ML models can be used in the identification of Rydberg atom configurations.