Needs further/better explaination
Since your label says “aws”, I assume your domain is hosted on route53. Use an ALB, per domain add a rule that matches the FQDN and forwards to a specific target group,which points to the ec2 machine and the publised container port.
Though, this seems to be a question about what needs to be done in AWS, rather then a docker question.
How to run multiple containers on a single host machine(123.564.789.564) and access the applications running on containers with dns NAME?
EX: docker run -d -p 8081:80 --name webserver nginx
dcoker run -d -p 8085:8080 --name appserver tomcat7
Now both the containers are running on the same host machine, now how to access them with dns names instead of ip:portno??