For example, I can change my username here on this instance. So long as my email id remains the same, my account is operable.
But GitHub doesn’t allow me to change my username. On top of that, GitHub forces an identifier on you when you create your username.
Where are you getting the idea that github is open source? GitHub CAN host open source software… and git is open source. GitHub is a website that allows people to upload content… and the source code is not open, and controlled by microsoft.
Now as far as whether usernames are changable on actual opensource websites… that’s also not a given. That’s a matter of if the software chooses to allow it. If the website doesn’t, you are welcome to take the source code, edit the source code to make it possible, and host your own copy of it. But nothing in open source inherently means you have any more control of an open source website that’s hosted outside of your machine/servers than a closed source one.