Neuroscientists have suggested that the mirror-neurons in our primate ancestors may have provided a substrate for the emergence of language in humans. Simulation studies of the emergence of language, using minimal implementations of proposed mechanisms, are a way to assess their explanatory power for the emergence and evolution of communication. In this work, we study the emergence and stability of linguistic labelling in a communities of agents with mirror-neuron mechanisms for associating deictic reference with speech utterances. These minimal agents possessing a built-in mirror-neuron style temporal recurrent neural network architecture are capable of perceiving and carrying out deixis (‘pointing’) to refer to others in their group, as well as producing and perceiving utterances of another agent in their group. They are able to generate and learn temporally extended phonetic utterances (‘names’) and associate these to deictic referents. Thus, the agents utter what they hear, and tend refer to the same entities as another agent that they watch when it points. Previous work has shown the emergence and stability of arbitrary names generated by the agents in certain fixed topologies of interaction. In this work, we systematically study the effects of different interaction topologies on the dynamics of convergence to a common vocabulary in the population, and its stability over time. Results show that certain topologies of interaction to be more conducive than others to the emergence of a stable vocabulary. Moreover, some topologies of interaction (such as cycles) are seen to yield instability and to amplify feedback given the mirror-neuron system. Linguistic convergence and change bear similarity to those of natural language. Homophony and multiple referents of particular proto-words may also emerge. In light of results, we suggest that mechanisms for confirming joint-attention and for suppression of mirroring could play an essential role in maintaining stability in the emergence of linguistic reference.