Is username auto-generated while registration?

It should be something they choose themselves when registering. If you’re not seeing it on your community, the most likely scenarios are 

• Username phrase has been customized to something else
• Something specific to using SSO

@DannyPancratz If that is the case, how do I change it at the backend?

Tell me if my understanding is right.

If it’s a SSO login, the username is assigned as per the phrase. I can change the username from the backend. 

Control > Customization > Phrasing

Search for username and you’ll see a lot of related phrases. 

That was just a hypothesis. I don’t know of any examples of usernames being assigned. My only guess is that it might be the case for some SSO instances. 

We use SSO and that is not the case for us. If someone is signing-in for the first time, it shows them the registration page where they pick a user name. But some SSO setups might automate random usernames. 

I’d recommend logging and out and trying to go through your new sign up flow to see what the experience is. Or contacting support for their help exploring your setup.