Had a reason to think about this problem,
The unique names which I've come across in my life were of those which were combination of words which are not part of colloquial vocabulary but is known to most native language speakers i.e. in my case Tamizh.
I was actually jealous of the unique tamizh names of my friends who got unique email ids, search results e.g. Priyanayagan (meaning: loved hero) , Samarasam (Meaning: Compromise, Usually in the sense of achievement of peace). There's no dearth of such vocabulary in Tamizh as it's the oldest living spoken language in the world.
So a better chance of finding unique baby names might to be look outside major spoken languages, Then again a name has huge societal/cultural and even legal implications and so just checking for uniqueness wouldn't be enough.