I just scanned over the TAPR and CERN open hardware licenses and I didn't see such a provision. My quick take on OHLs is that they are specifications for building the hardware - and therefore, information - not the hardware itself. And it only makes sense when we consider the incredibly expensive and complicated (from an experimenter's point of view) infrastructure that is a chip foundry necessary to create the kinds of hardware we take for granted and have reduced to commodity parts, CPUs, & MCUs being a prime example.
Thus "Arduino" is an open source specification for building microcontroller boards or board-sets based on ATMEL MCU chips, as well as the products of the Italian company SmartProjects. That is why there are so-called Arduino clones, otherwise, why wouldn't any clone of an Arduino be an Arduino?