To access the EC2 instance with your own domain, assigning a static global IP address and setting up a DNS server are necessary.
Elastic IP assignment creates a fixed global IP address to your instance.
Once you obtain your domain name (from a different provider), go to AWS Route 53 which is a DNS web service. It's a good match with AWS since it's compatible with all its services.
The documentation of using Route 53 is found here Assign own domain (Route 53) and setting of Elastic IP.

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