By definition, authentication is the act of proving the identity of a user. For example, 'root' is a known user name on every Linux system. If a server grants access to any user presenting themselves as 'root', there is no authentication taking place; merely identification. And the identity itself is typically not a secret. For example, the /etc/passwd file that lists all local usernames is readable for all users.
Conventionally, authentication takes place after the identification step and involves the use of one or more authentication factors - something the user knows (like a password), something the user has (like an SSH key) or the something the user is/does (like a fingerprint). You can refer to the Wikipedia page for a lot more info: https://en.wikipedia.org/wiki/Authentication
With SSH, the closest approximation you can make is to use an account with an empty or blank password. Then you could use AuthenticationMethods none and PermitEmptyPasswords yes (in sshd_config), and you should be able to log in with the username and a blank password. Globally setting these options would be unwise; it is better to use a Match block and apply these settings to a specific user or user group. Since the user name is the only line of defense, it would also make sense to use a new, non-standard username. See the manpage for more details on the options: sshd_config(5)
Again, this approach is unsafe from a security perspective as you're cutting out authentication entirely. And depending upon the privileges allowed to the password-less user account, you will open yourself up to further vulnerabilities. Review your requirements carefully and decide if you would like to proceed.