If you want specifically a cryptographic/indexing hash, where 1 bit of change in input changes ~50% of bits in the output, then that's one possible goal/restriction. But that's just one kind of hash function.

But you can have hash functions with the goal of preserving similarity. For example soundex is a hash function with that constraint. From: https://pdfs.semanticscholar.org/06d6/8587c27058dd6ab3fb8238...

> For example value 1 = "Damieva" and value 2 = "Dameiva." These two values will produce the same Soundex hash value, creating a match.

There's also the whole class of LSH https://en.wikipedia.org/wiki/Locality-sensitive_hashing