Requesting an AWS issued public certificate for a domain name is straightforward in the ACM console and DNS validation can be done automatically if your domain is also on Route 53.
Tag: Route53
Setting up and using a custom Sub Domain with the AWS Cognito Hosted UI
How to setup a custom sub domain for your Cognito Pool’s Hosted UI.
Creating a custom domain name for an AWS AppSync API endpoint using Cloudformation
How to front the AWS generated AppSync API endpoint with a custom domain name using Cloudformation.