Private API gateway route with Flask app

Serverless Framework
1

I’m creating an API that parses a name into its separate parts. I want to require an API key on AWS. The function in my flask app looks like this:

# app.py
@app.route('/names/<name>', methods=['GET'])
def convert_name(name):
    # do stuff

I noticed that this works to return a valid API response, but does not set the API to private.

# serverless.yml
functions:
  app:
    handler: wsgi_handler.handler
    events:
      - http: 'GET /names/{proxy+}'
        private: true

So I changed the file to this:

# serverless.yml
functions:
  app:
    handler: wsgi_handler.handler
    events:
      - http:
          path: names/{proxy+}
          method: get
          private: true

This sets the route to private like I want, but now the routing is messed up and all I get is a 404 when sending a valid input such as /names/John M. Glenn.

Any idea what I am doing wrong here?