The Naming Games (NG) are agent-based models for agreement dynamics, peer pressure and herding in social networks, and protocol selection in autonomous ad-hoc sensor networks. By introducing a small noise term to the NG, the resulting Markov Chain model called Noisy Naming Games (NNG) are ergodic, in which all partial consensus states are recurrent. By using Gibbs-Markov equivalence we show how to get the NNG's stationary distribution in terms of the local specification of a related Markov Random Field (MRF). By ordering the partially-synchronized states according to their Gibbs energy, taken here to be a good measure of social tension, this method offers an enhanced method for community-detection in social interaction data. We show how the lowest Gibbs energy multi-name states separate and display the hidden community structures within a social network.