Real-world AI systems are tackling increasingly complex problems, often through interactions among large language model (LLM) agents. When these agents develop inconsistent conventions, coordination can break down. Applications such as collaborative coding and distributed planning therefore require reliable, consistent communication, and scalability is a central concern as systems grow. We introduce Schema-Induced Games for Naming (SIGN), a naming game that examines how lightweight structure can steer convention formation. We compare schema-induced communication to unconstrained natural language and find faster convergence with up to 5.8x higher agreement. These results suggest that minimal structure can act as a simple control knob for efficient multi-agent coordination, pointing toward broader applications beyond the naming game.