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?
Yes.
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?
Most of this can be found reading through different Git docs, whether from GitHub, GitLab, Codeberg, Gitea, etc. When using Git you can use different keys for different repos/forges and each has a defined pair, similar to accessing different SSH servers that require specific key pairs. I do understand your questions, but I lack the finesse to explain it since I really only use SSH and Git for my blog and not for anything too complicated.