This method is known as creating a digital signature of the message. It ensures the integrity of the message by verifying that it has not been tampered with in transit. The process involves hashing the message and encrypting the hash value with the sender's private key. Any changes to the message will result in a different hash value1. This method is used in DomainKeys Identified Mail (DKIM), which verifies an email's domain and helps show that the email has not been tampered with in transit2.
References:
Understanding Digital Signatures | CISA
Using DomainKeys Identified Mail (DKIM) in your organisation