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This is like that Catalonia hashed database for voter identification that ended up outing national ID / birthday / zipcode associations. Hashes aren't magical pixie dust. If the search space is bruteforceable, they amount to the illusion of security.
If you *must* do this (and understand the risks), either use full legal names to maximize entropy and a very strong salted hash, like say bcrypt/scrypt tuned to take 5 seconds per hash on a CPU, or similar...
... or use a very *weak* hash, like the 6-digit prefix of the SHA1 (24 bits), to guarantee collisions and thus make it a probabilistic filter and not something you could brute force usefully.
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