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We describe a fully abstract semantics for a simple functional language with locally declared names which may be used as pointers to names. It is based on a category of dialogue games acted upon by the group of natural number automorphisms. This allows a formal, semantic characterization of the key properties of names such as freshness and locality. We describe a model of the call-by-value λ-calculus (a closed Freyd category) based on these games, and show that it can be used to interpret thedoi:10.1016/j.apal.2007.10.006 fatcat:twc3zxtizvajvnwhvrdn3sqgsi