How is the public key distributed in an orderly, controlled fashion so that the users can be sure of the sender's identity?

A hash value is a fixed-length digest used to verify data integrity, not to distribute or bind a public key to an identity.

A private key is kept secret by its owner and is never distributed; it is the paired counterpart to the public key.

A digital signature proves the authenticity and integrity of a message using the sender's private key, but it does not itself distribute or bind the public key to a verified identity.

A digital certificate is issued by a trusted Certificate Authority (CA) that cryptographically vouches for the association between a public key and its owner's identity. Recipients verify the CA's signature on the certificate to confirm the public key genuinely belongs to the claimed sender. This PKI-based mechanism is the standard method for distributing public keys in an orderly, trusted manner.