I was able to change this from amazoncognito.com to domain.io by doing the following:

1. AWS / User Pools / App Integration / Domain Name

• Set a domain name, ie: oauth.sandbox.domain.io
• Create an AWS Managed Certificate for this domain name
• The AWS account I was working with has a sandbox.domain.io route53 Hosted Zone, so adding dns verifications and A record aliases was easy.

When the ACM and domain name are added, I was given a cloudfront url. Add this in your route53 hosted zone as an A record Alias.

2. Google Cloud Config

• Update your Api Credentials to add oauth.sandbox.domain.io to your Authorized JavaScript Origins and Authorized redirect URIs.
• Update your OAuth Consent Screen so your Authorized Domains include domain.io.

3. Cognito Client App

• Update it to use oauth.sandbox.domain.io instead of ${domain_prefix}.auth.${region}.amazoncognito.com