I've generated a pair of keys with PuttyGen and I use it to connect to a remote server with Putty and SSH.
What surprises me is that, when configuring the public key authentication, at no moment I had to provide a login. The only moment I had to do that is when I had to log in the server to update the file .ssh/authorized_keys. But that log-in could have been done with any user that has the right to update that file.
I've checked the content of the public/private keys and the file authorized_keys, I've seen no info about the login.
When I log in, the login is asked then directly the server seems to look for a public key linked to that login. Where does it look for that link ?