What is the name of the process that is used to establish whether or not a user's identity is legitimate?

Authentication

Explanation:

The authentication process is used to check the identification of the particular user or computer system. we can give authentication to any user by the username and password. If a particular user puts the correct username and password into the website then it has the authority to access that particular website.

For example: In the any mail website, if a particular user login with the correct username and password then it has an authenticated user. It means it has the right to access the mail of that account.