Linux

I was reading GitLab's documentation (see link) on how to write to a repository from within the CI pipeline and noticed something: The described Docker executor is able to authenticate e.g. against the Git repository with only a private SSH key, being told absolutely nothing about the user's name it is associated with.
If I'm correct, that would mean that technically, I could authenticate to an SSH server without supplying my name if I use a private key?

I know that when I don't supply a user explicitly like ssh user@server or via .ssh/config, the active environment's user is used automatically, that's not what I'm asking.

The public key contains a user name/email address string, I'm aware, is the same information also encoded into the private key as well? If yes, I don't see the need to hand that info to an SSH call. If no, how does the SSH server know which public key it's supposed to use to challenge my private key ownership? It would have to iterate over all saved keys, which sounds rather inefficient to me and potentially unsafe (timing attacks etc.).

I hope I'm somewhat clear, for some reason I find it really hard to phrase this question.