The street address is officially registered, is attributed by the town and doesn’t belong to you. I don’t think you can find some more public than that.
Compare that to the name of your private router that happens to be broadcasted far outside your house for technical reasons.
I doubt you can claim "ownership" of text strings used for wifi and otherwise freely available. I suspect Google's lawyers would have stopped this feature from being implemented if there were even potential issues.
You are right in that there isn't an ownership angle to this. The same way if you call your cat "Murphy", you wouldn't get a claim on the name, nor should forbid people from memorizing that you call your cat that name.
To be honest I am not sure where I stand on the issue, but I sympathize on the uneasiness of a global corporation taking advantage of a situation in a way few people ever thought about. That's where I think the perception of the public/private status diverge for most people.
Compare that to the name of your private router that happens to be broadcasted far outside your house for technical reasons.