Route53 can be used to create an alias with your domain name. If you visit the service console at https://console.aws.amazon.com/route53, and click on the hosted zones menu, you can add a new hosted zone for your domain name, which is an alias to the ELB previously set.
Assuming that you already own the domain name from a registrar, you can simply redirect the domain to AWS's DNS. Click on Create Hosted Zone, and add your domain.
Once it is created, you can go to Create a Record Set, and select a type A record. The record has to be an Alias, and in the target input, a dropdown appears with the list of available targets:
The ELB load balancer that was previously created by the wizard should appear in that list, and selecting it links your domain name to that ELB:
This step is all it takes to link a domain name to your deployed ECS cluster; and you can add more entries...
