The device really should implement speaker identification before accepting commands, yeah. Seems like a task a machine learning focused company like Google really should be able to accomplish.
Just allow every buyer to give the device their own unique wake name.
So if people have to choose their own, they'll have to choose one that is also not easily mistaken. Something tells me that would be a very annoying process.
It's not that they chose those keywords for uniqueness, they chose them for branding purposes.
[0] https://support.google.com/nexus/answer/6093922 - last entry.
It worked quite well, I don't know why Google Home doesn't have anything like this.
I watched Sneakers recently and I think it really holds up.