To connect a domain or service to your Mac, update the appropriate DNS records at your DNS provider so the hostname resolves to the public IP or network entry used by the service running on the Mac. DNS alone is only part of the process; the application must also be configured correctly on the system.
For websites, APIs, or internal tools, you may also need a reverse proxy, SSL certificate, firewall allowance, and the correct service binding on the Mac itself.
Test the application locally first, then test externally after the DNS change.