I've heard people suggest that before. I don't buy it.
Cross-fit is extremely popular right now. I don't think anyone is hearing that and thinking, "Damn, I do want to get that Jesus body..." "Cross" on it's own just doesn't resonate as that religious.
I agree on your example of Gameboy. It was a brand that had such a momentum that anyone playing a handheld device might be playing a "Gameboy" because was just ubiquitous with that type of system. But I disagree on the Nintendo Entertainment System. While plenty of people called it the NES, and eventually the SNES with the next iteration, as a full name, it was always the Nintendo and Super Nintendo. "Nintendo" is the brand that has cache. If it's a system, I think the Nintendo for the console and Nintendo Mobile/Handled/etc for the handheld would make sense.
Oh yeah, Nintendo is a name people still recognize even if some don't even know what their current hardware is. Their name should definitely be front and center in their naming conventions. They just need to look back at how they handled things before like their Gameboy brand on what they should do.