Add the Github IPs as A records on Namecheap.
185.199.108.153
185.199.109.153
185.199.110.153
185.199.111.153
Add your Github domain as the CNAME alias on Namecheap. your_username.github.io
Add a CNAME with your new domain name in your repository, lowercase and nothing else.
Tutorial: https://youtu.be/FBtehan5DAo