Short answer -- you are logging-in (or accessing Github) as yourself.
Mild detail: you are accessing as the identity authenticated by the SSH key-pair you used.
To access Github over the web (browser) you use a username/password combination. Whereas, when accessing over SSH you have not used your password or for that matter your username. How is your identity authenticated then(?) you ask.
That is where the SSH key pair comes in. I am going to explain how the key-pair replaces username/password here without going into details of how it works (there is ample documentation on that).
To keep this answer simple, we can think of your SSH public-key as the username which will be authenticated with the matching SSH private-key that acts like the password. While the way SSH works is different from how username/password work, the outcome is similar (you are identified and authenticated by Github).
Github uses the generic
git username to accomplish this SSH based authentication.
You configured that public-key in your Github account after logging in with your username/password based access. This is an action restricted to that secured access. Only someone with that access could have setup the public-key.
The private-key matching that public key (your password in this discussion) is safely on the password protected login from where you are firing the git clone command.
So, when you invoke git over SSH from your login, the SSH protocol works to let Github confirm that this access is being made by the owner of the public-key setup in your account there. Transitively, the owner of that Github account.