Custom display name after IdP first login

Hello, I’ve configured regular username+password+email registration together with social providers, however with social providers, i.e google, after logging in the username and email both are set to the email. I want to give the user ability to input their preferred display name after they log in with the social provider for the first time.
So far I have realized that I should override the first login flow but no authentication flow gives me the ability to do this. How should I approach this issue? Do I have to create custom authenticator and also provide custom visual templates to be displayed for this?