Cultural innovation (e.g., music, beliefs, language) tends to be adopted regionally. The geographic area where innovation is adopted is often attributed to one of two factors: (i) speakers adopting new behaviors that signal their demographic identities (i.e., an identity effect), or (ii) these behaviors spreading through homophilous networks (i.e., a network effect). In this study, we show that network and identity play complementary roles in determining where new language is adopted; thus, modeling the diffusion of lexical innovation requires incorporating both network and identity. We develop an agent-based model of cultural adoption, and validate geographic properties in our simulations against a dataset of innovative words that we identify from a 10% sample of Twitter (e.g., fleeky, birbs, ubering). Using our model, we are able to directly test the roles of network and identity by comparing a model that combines network and identity against simulated network-only and identity-only counterfactuals. We show that both effects influence different mechanisms of diffusion. Specifically, network principally drives spread among urban counties via weak-tie diffusion, while identity plays a disproportionate role in transmission among rural counties via strong-tie diffusion. Diffusion between urban and rural areas, a key component in innovation spreading nationally, requires both network and identity. Our work suggests that models must integrate both factors in order to understand and reproduce the adoption of innovation.