I've searched through Go Daddy, eNom, Network Solutions (prior to what they
are doing now), even Moniker and NameCheap. Some were available, others
were taken, but not all were registered a few minutes after lookup.
While registrars can guarantee they don't sell their queries or don't register all
those searched domain names for themselves, they can't guarantee no one is
going to "steal your searches". I'm simply pointing this out so you don't have
any unrealistic expectations.