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 output used to verify data integrity, not a mechanism for distributing or authenticating public keys.

The private key is kept secret by its owner and never distributed - sharing it would completely compromise the asymmetric key pair.

A digital signature uses the sender's private key to sign data and proves message integrity and non-repudiation, but it does not itself distribute or certify a public key in a controlled fashion.

A digital certificate is issued by a trusted Certificate Authority (CA) and cryptographically binds a public key to an entity's identity. This controlled distribution model allows recipients to verify the authenticity of the public key and, by extension, confirm the sender's identity before trusting communications or signatures.