I have gcloud inside my cloudbuild.yaml how could I make the deployed name something that I want? It looks it is like https://[Project Name].ey.r.appspot.com/ but I want to have it like https://MyNameappspot.com/
Should I do it inside app.yaml?
You can help determine the URL that e.g. App Engine apps will use but there are constraints on how your apps' subdomain names are determined.
See App Engine How Requests are Routed for an explanation.