I'm not sure what you mean by hash, but i6 think you're trying to describe mutual authentication, where the service also authenticates itself to the user. Look up things like pake, srp, and tls client certificates for more information.

https://en.m.wikipedia.org/wiki/Mutual_authentication

https://en.m.wikipedia.org/wiki/Secure_Remote_Password_proto...

https://en.m.wikipedia.org/wiki/Password-authenticated_key_a...

https://en.m.wikipedia.org/wiki/Client_certificate