How do people talk about things they've never talked about before? One view suggests that a new shared naming system establishes an arbitrary link to a specific target, like proper names that cannot extend beyond their bearers. An alternative view proposes that forming a shared way of describing objects involves broader conceptual alignment, reshaping each individual's semantic space in ways that should generalize to new referents. We test these competing accounts in a dyadic communication study (N=302) leveraging the recently-released KiloGram dataset containing over 1,000 abstract tangram images. After pairs of participants coordinated on referential conventions for one set of images through repeated communication, we measured the extent to which their descriptions aligned for undiscussed images. We found strong evidence for generalization: partners showed increased alignment relative to their pre-test labels. Generalization also decayed nonlinearly with visual similarity (consistent with Shepard's law) and was robust across levels of the images' nameability. These findings suggest that ad hoc conventions are not arbitrary labels but reflect genuine conceptual coordination, with implications for theories of reference and the design of more adaptive language agents.