  We examine a variant of the Naming Game, where agents having several words
communicate more often than single-word agents. Depending on the preference and
dimensionality, the model either converges to a single-language state as in an
ordinary Naming Game or remains in a disordered, multi-language phase. At the
transition point separating these regimes, due to a percolation-like process,
the model converges to a single-language state but much faster than in the
ordinary naming game. We also show that the coarsening dynamics of the ordinary
Naming Game is slower than expected due to stripe structures that sometimes
spontaneously form during the evolution of the model.
