generic.py

from oauthenticator.generic import GenericOAuthenticator

class CustomAuthenticator(GenericOAuthenticator):
  async def authenticate(self, handler, data=None):
    resp = await super().authenticate(handler, data)
    # resp is a dict mentioned here: https://github.com/jupyterhub/oauthenticator/blob/master/oauthenticator/generic.py#L163
    # modify it as you wish, set username key
    modified_resp = resp.copy()
    modified_resp['username'] = resp['auth_state']['oauth_resp']['attrib']['email']
    return modified_resp

values.yaml

hub:
  extraConfig: 
   01-custom-auth: |
      <copy-the generic.py here>
      
      c.JupyterHub.authenticator_class = CustomAuthenticator